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.
ScanSolve AI Answer
Here are the solutions to the problems from the image. Problem 1 (unnumbered): The area of a triangle is 36 cm^2. If its base is 6 cm, what is its height? Step 1: Write the formula for the area of a triangle. The area of a triangle (A) is given by: A = (1)/(2)bh where b is the base and h is the height. Step 2: Substitute the given values into the formula. Given A = 36 cm^2 and b = 6 cm. 36 = (1)/(2) × 6 × h Step 3: Solve for the height (h). 36 = 3h h = (36)/(3) h = 12 cm The height of the triangle is 12 cm. --- Question 39: The area of a triangle is 100 cm^2. If its base is 20 cm, what is its height? Step 1: Write the formula for the area of a triangle. A = (1)/(2)bh Step 2: Substitute the given values into the formula. Given A = 100 cm^2 and b = 20 cm. 100 = (1)/(2) × 20 × h Step 3: Solve for the height (h). 100 = 10h h = (100)/(10) h = 10 cm The height of the triangle is 10 cm. --- Question 40: The area of a triangle is 32 cm^2. If its base is 8 cm, what is its height? Step 1: Write the formula for the area of a triangle. A = (1)/(2)bh Step 2: Substitute the given values into the formula. Given A = 32 cm^2 and b = 8 cm. 32 = (1)/(2) × 8 × h Step 3: Solve for the height (h). 32 = 4h h = (32)/(4) h = 8 cm The height of the triangle is 8 cm. --- Question 41: The side of a square field is 40 cm. Find its perimeter and area. Step 1: Write the formulas for the perimeter and area of a square. For a square with side length s: Perimeter (P) = 4s Area (A) = s^2 Step 2: Substitute the given side length into the formulas. Given s = 40 cm. Perimeter: P = 4 × 40 cm Area: $A = (40 cm)^