Problem 4: Find the perimeter of the triangle below:

Here are the solutions for problems 4 and 5. Problem 4: Find the perimeter of the triangle below: The tick marks on two sides of the triangle indicate that these sides are equal in length. Therefore, 2x - 4 = x + 8. Step 1: Solve for x. 2x - 4 = x + 8 Subtract x from both sides: 2x - x - 4 = 8 x - 4 = 8 Add 4 to both sides: x = 8 + 4 x = 12 Step 2: Calculate the length of each side of the triangle. Side 1: 2x - 4 = 2(12) - 4 = 24 - 4 = 20 cm Side 2: x + 8 = 12 + 8 = 20 cm Side 3: 3x + 11 = 3(12) + 11 = 36 + 11 = 47 cm Step 3: Calculate the perimeter of the triangle. The perimeter is the sum of all side lengths. Perimeter = Side 1 + Side 2 + Side 3 Perimeter = 20 cm + 20 cm + 47 cm Perimeter = 87 cm The perimeter of the triangle is 87 cm. Problem 5: The figure below is a rectangle. Study it and answer the questions that follow. The question is incomplete as it does not specify what to find. We will assume the questions are to find the value of x, the dimensions of the rectangle, its perimeter, and its area. In a rectangle, opposite sides are equal in length. From the tick marks, the top side is equal to the bottom side. So, 5x + 5 = x + 27. Step 1: Solve for x. 5x + 5 = x + 27 Subtract x from both sides: 4x + 5 = 27 Subtract 5 from both sides: 4x = 27 - 5 4x = 22 Divide by 4: x = (22)/(4) x = 5.5 Step 2: Calculate the dimensions (length and width) of the rectangle. Length (L): 5x + 5 = 5(5.5) + 5 = 27.5 + 5 = 32.5 cm (Check with bottom side: x + 27 = 5.5 + 27 = 32.5 cm) Width (W): 2x = 2(5.5) = 11 cm Step 3: Calculate the perimeter of the rectangle. Perimeter = 2(L + W) Perimeter = 2(32.5 cm + 11 cm) Perimeter = 2(43.5 cm) Perimeter = 87 cm Step 4: Calculate the area of the rectangle. Area = L × W Area = 32.5 cm × 11 cm Area = 357.5 cm^2 For the rectangle: Value of x: 5.5 Length: 32.5 cm Width: 11 cm Perimeter: 87 cm Area: 357.5 cm^2 3 done, 2 left today. You're making progress.