The homework involves calculating the area and width of rectangles and the area of a square given its perimeter. It also includes a table completion task for rectangle dimensions.

Question

Asked on April 5, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-04-05T13:05:54.218Z

Here are the solutions to the problems: Table Completion: Row 1: Length = 3 cm, Width = 6 cm Area = Length × Width = 3 cm × 6 cm = 18 cm^2 Row 2: Length = 8 m, Width = 15 m Area = Length × Width = 8 m × 15 m = 120 m^2 Row 3: Width = 9 mm, Area = 36 mm^2 Length = Area ÷ Width = 36 mm^2 ÷ 9 mm = 4 mm Row 4: Length = 10 km, Area = 15 km^2 Width = Area ÷ Length = 15 km^2 ÷ 10 km = 1.5 km --- 2. If the length of a rectangle is 36 cm and the area is 720 cm^2, what is the width of the rectangle? Step 1: Write down the given values and the formula for the area of a rectangle. L = 36 cm A = 720 cm^2 A = L × W Step 2: Rearrange the formula to solve for the width (W). W = (A)/(L) Step 3: Substitute the given values into the formula and calculate. W = 720 cm^236 cm W = 20 cm The width of the rectangle is 20 cm. --- 3. What is the area of a square with a perimeter of 44 m? Step 1: Write down the given perimeter and the formula for the perimeter of a square. P = 44 m P = 4s where s is the side length of the square. Step 2: Solve for the side length (s). s = (P)/(4) s = 44 m4 s = 11 m Step 3: Calculate the area of the square using the formula A = s^2. A = (11 m)^2 A = 121 m^2 The area of the square is 121 m^2. --- 4. A square having length 6 m has the same perimeter as a rectangle. Find the area of the rectangle if its length is 4 cm longer than its width. Assumption: The length of the rectangle is 4 meters longer than its width, to maintain consistent units with the square's dimensions. Step 1: Calculate the perimeter of the square. Side length of square s = 6 m. Perimeter of square P_square = 4s = 4 × 6 m = 24 m. Step 2: The perimeter of the rectangle is the same as the square. Perimeter of rectangle P_rect = 24 m. Let the length of the rectangle be L and the width be W. We are given L = W + 4 m. The formula for the perimeter of a rectangle is P_rect = 2(L+W). Step 3: Substitute the expressions for P_rect and L into the perimeter formula and solve for W. 24 = 2((W+4) + W) 24 = 2(2W + 4) 12 = 2W + 4 12 - 4 = 2W 8 = 2W W = (8)/(2) W = 4 m Step 4: Calculate the length L. L = W + 4 m L = 4 m + 4 m L = 8 m Step 5: Calculate the area of the rectangle. A_rect = L × W A_rect = 8 m × 4 m A_rect = 32 m^2 The area of the rectangle is 32 m^2. --- 5. The length of a rectangle is twice its width. If its area is 288 cm^2, find the length of the rectangle. Step 1: Write down the given information. Let the width of the rectangle be W. The length L = 2W. Area A = 288 cm^2. Step 2: Use the area formula A = L × W and substitute L = 2W. 288 = (2W) × W 288 = 2W^2 Step 3: Solve for W. W^2 = (288)/(2) W^2 = 144 W = sqrt(144) W = 12 cm Step 4: Calculate the length L. L = 2W L = 2 × 12 cm L = 24 cm The length of the rectangle is 24 cm. --- 6. The figure shows a hole cut in the middle of a cardboard. Calculate the shaded area. Step 1: Identify the dimensions of the outer square and the inner square (hole). Outer square side length = 10 cm. Inner square side length = 4 cm. Step 2: Calculate the area of the outer square. Area of outer square A_outer = side × side = 10 cm × 10 cm = 100 cm^2. Step 3: Calculate the area of the inner square (the hole). Area of inner square A_inner = side × side = 4 cm × 4 cm = 16 cm^2. Step 4: Calculate the shaded area by subtracting the inner area from the outer area. Shaded Area = A_outer - A_inner Shaded Area = 100 cm^2 - 16 cm^2 Shaded Area = 84 cm^2 The shaded area is 84 cm^2. --- 7. PQRS is a square of length 12 cm. A square LMNS of area 25 cm^2 is removed from it. What will be the length of LP? Step 1: Determine the side length of square PQRS. Side length of PQRS, s_1 = 12 cm. So, PS = 12 cm. Step 2: Determine the side length of square LMNS. Area of LMNS, A_2 = 25 cm^2. Side length of LMNS, s_2 = sqrt(A_2) = sqrt(25 cm)^2 = 5 cm. From the diagram, S is a common vertex, and L is on PS. Thus, SL is a side of the square LMNS. So, SL = 5 cm. Step 3: Calculate the length of LP. LP = PS - SL LP = 12 cm - 5 cm LP = 7 cm The length of LP is 7 cm. --- 8. The area of a square is twice the area of a rectangle with dimensions 45 cm and 10 cm. Find the length of the square. Step 1: Calculate the area of the rectangle. Length of rectangle L_rect = 45 cm. Width of rectangle W_rect = 10 cm. Area of rectangle A_rect = L_rect × W_rect = 45 cm × 10 cm = 450 cm^2. Step 2: Calculate the area of the square. Area of square A_square = 2 × A_rect A_square = 2 × 450 cm^2 = 900 cm^2. Step 3: Find the length of the square's side (s). For a square, A_square = s^2. s = sqrt(A_square) s = sqrt(900 cm)^2 s = 30 cm The length of the square is 30 cm. --- 9. The width of a rectangle is 4 cm less than its length and its perimeter is 48 cm. Find its area. Step 1: Define the length and width in terms of a single variable. Let the length of the rectangle be L. The width W = L - 4 cm. Step 2: Use the given perimeter and the perimeter formula. Perimeter P = 48 cm. P = 2(L+W). Step 3: Substitute W = L-4 into the perimeter formula and solve for L. 48 = 2(L + (L-4)) 48 = 2(2L - 4) 24 = 2L - 4 24 + 4 = 2L 28 = 2L L = (28)/(2) L = 14 cm Step 4: Calculate the width W. W = L - 4 cm W = 14 cm - 4

Accepted Answer · 2026-04-05T13:05:54.218Z

Here are the solutions to the problems: Table Completion: Row 1: Length = 3 cm, Width = 6 cm Area = Length × Width = 3 cm × 6 cm = 18 cm^2 Row 2: Length = 8 m, Width = 15 m Area = Length × Width = 8 m × 15 m = 120 m^2 Row 3: Width = 9 mm, Area = 36 mm^2 Length = Area ÷ Width = 36 mm^2 ÷ 9 mm = 4 mm Row 4: Length = 10 km, Area = 15 km^2 Width = Area ÷ Length = 15 km^2 ÷ 10 km = 1.5 km --- 2. If the length of a rectangle is 36 cm and the area is 720 cm^2, what is the width of the rectangle? Step 1: Write down the given values and the formula for the area of a rectangle. L = 36 cm A = 720 cm^2 A = L × W Step 2: Rearrange the formula to solve for the width (W). W = (A)/(L) Step 3: Substitute the given values into the formula and calculate. W = 720 cm^236 cm W = 20 cm The width of the rectangle is 20 cm. --- 3. What is the area of a square with a perimeter of 44 m? Step 1: Write down the given perimeter and the formula for the perimeter of a square. P = 44 m P = 4s where s is the side length of the square. Step 2: Solve for the side length (s). s = (P)/(4) s = 44 m4 s = 11 m Step 3: Calculate the area of the square using the formula A = s^2. A = (11 m)^2 A = 121 m^2 The area of the square is 121 m^2. --- 4. A square having length 6 m has the same perimeter as a rectangle. Find the area of the rectangle if its length is 4 cm longer than its width. Assumption: The length of the rectangle is 4 meters longer than its width, to maintain consistent units with the square's dimensions. Step 1: Calculate the perimeter of the square. Side length of square s = 6 m. Perimeter of square P_square = 4s = 4 × 6 m = 24 m. Step 2: The perimeter of the rectangle is the same as the square. Perimeter of rectangle P_rect = 24 m. Let the length of the rectangle be L and the width be W. We are given L = W + 4 m. The formula for the perimeter of a rectangle is P_rect = 2(L+W). Step 3: Substitute the expressions for P_rect and L into the perimeter formula and solve for W. 24 = 2((W+4) + W) 24 = 2(2W + 4) 12 = 2W + 4 12 - 4 = 2W 8 = 2W W = (8)/(2) W = 4 m Step 4: Calculate the length L. L = W + 4 m L = 4 m + 4 m L = 8 m Step 5: Calculate the area of the rectangle. A_rect = L × W A_rect = 8 m × 4 m A_rect = 32 m^2 The area of the rectangle is 32 m^2. --- 5. The length of a rectangle is twice its width. If its area is 288 cm^2, find the length of the rectangle. Step 1: Write down the given information. Let the width of the rectangle be W. The length L = 2W. Area A = 288 cm^2. Step 2: Use the area formula A = L × W and substitute L = 2W. 288 = (2W) × W 288 = 2W^2 Step 3: Solve for W. W^2 = (288)/(2) W^2 = 144 W = sqrt(144) W = 12 cm Step 4: Calculate the length L. L = 2W L = 2 × 12 cm L = 24 cm The length of the rectangle is 24 cm. --- 6. The figure shows a hole cut in the middle of a cardboard. Calculate the shaded area. Step 1: Identify the dimensions of the outer square and the inner square (hole). Outer square side length = 10 cm. Inner square side length = 4 cm. Step 2: Calculate the area of the outer square. Area of outer square A_outer = side × side = 10 cm × 10 cm = 100 cm^2. Step 3: Calculate the area of the inner square (the hole). Area of inner square A_inner = side × side = 4 cm × 4 cm = 16 cm^2. Step 4: Calculate the shaded area by subtracting the inner area from the outer area. Shaded Area = A_outer - A_inner Shaded Area = 100 cm^2 - 16 cm^2 Shaded Area = 84 cm^2 The shaded area is 84 cm^2. --- 7. PQRS is a square of length 12 cm. A square LMNS of area 25 cm^2 is removed from it. What will be the length of LP? Step 1: Determine the side length of square PQRS. Side length of PQRS, s_1 = 12 cm. So, PS = 12 cm. Step 2: Determine the side length of square LMNS. Area of LMNS, A_2 = 25 cm^2. Side length of LMNS, s_2 = sqrt(A_2) = sqrt(25 cm)^2 = 5 cm. From the diagram, S is a common vertex, and L is on PS. Thus, SL is a side of the square LMNS. So, SL = 5 cm. Step 3: Calculate the length of LP. LP = PS - SL LP = 12 cm - 5 cm LP = 7 cm The length of LP is 7 cm. --- 8. The area of a square is twice the area of a rectangle with dimensions 45 cm and 10 cm. Find the length of the square. Step 1: Calculate the area of the rectangle. Length of rectangle L_rect = 45 cm. Width of rectangle W_rect = 10 cm. Area of rectangle A_rect = L_rect × W_rect = 45 cm × 10 cm = 450 cm^2. Step 2: Calculate the area of the square. Area of square A_square = 2 × A_rect A_square = 2 × 450 cm^2 = 900 cm^2. Step 3: Find the length of the square's side (s). For a square, A_square = s^2. s = sqrt(A_square) s = sqrt(900 cm)^2 s = 30 cm The length of the square is 30 cm. --- 9. The width of a rectangle is 4 cm less than its length and its perimeter is 48 cm. Find its area. Step 1: Define the length and width in terms of a single variable. Let the length of the rectangle be L. The width W = L - 4 cm. Step 2: Use the given perimeter and the perimeter formula. Perimeter P = 48 cm. P = 2(L+W). Step 3: Substitute W = L-4 into the perimeter formula and solve for L. 48 = 2(L + (L-4)) 48 = 2(2L - 4) 24 = 2L - 4 24 + 4 = 2L 28 = 2L L = (28)/(2) L = 14 cm Step 4: Calculate the width W. W = L - 4 cm W = 14 cm - 4

The homework involves calculating the area and width of rectangles and the area of a square given its perimeter. It also includes a table completion task for rectangle dimensions.

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The homework involves calculating the area and width of rectangles and the area of a square given its perimeter. It also includes a table completion task for rectangle dimensions.

Need help with your own homework?

More Mathematics Questions