Question

The perimeter of two squares are 40 cm and 32 cm. The perimeter of a third square whose area is equal to the difference of the areas of the two squares is :

• A. 36 cm
• B. 24 cm
• C. 16 cm
• D. 40 cm

Hint:

Remember the formulas for the perimeter and area of a square: Perimeter = \( 4 \times \text{side} \), Area = \( (\text{side})^2 \). Work step-by-step to find the required dimensions of the third square.

Answer 1

The Correct Option is B

Step 1: Find the side length of the first square.
Perimeter of the first square = 40 cm
Side length of the first square (\(s_1\)) = \( \frac{\text{Perimeter}}{4} = \frac{40}{4} = 10 \) cm
Step 2: Find the area of the first square.
Area of the first square (\(A_1\)) = \( s_1^2 = 10^2 = 100 \) sq cm Step 3: Find the side length of the second square.
Perimeter of the second square = 32 cm
Side length of the second square (\(s_2\)) = \( \frac{\text{Perimeter}}{4} = \frac{32}{4} = 8 \) cm
Step 4: Find the area of the second square.
Area of the second square (\(A_2\)) = \( s_2^2 = 8^2 = 64 \) sq cm Step 5: Find the area of the third square.
Area of the third square (\(A_3\)) = Difference of the areas of the first two squares = \( |A_1 - A_2| = |100 - 64| = 36 \) sq cm Step 6: Find the side length of the third square.
Side length of the third square (\(s_3\)) = \( \sqrt{A_3} = \sqrt{36} = 6 \) cm Step 7: Find the perimeter of the third square.
Perimeter of the third square = \( 4 \times s_3 = 4 \times 6 = 24 \) cm