Question

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

• A. 24
• B. 48
• C. 40
• D. 32
• E.

Hint:

For squares, use the formula \( P = 4a \) for the perimeter and \( \text{Area} = a^2 \) for the area. Calculate the difference in areas and then find the perimeter of the third square.

Answer 1

The Correct Option is A

Step 1: The perimeter of a square is given by \( P = 4a \), where \( a \) is the side length. For the first square, the perimeter is 40 cm, so the side length is: \[ a_1 = \frac{40}{4} = 10 \, \text{cm}. \] For the second square, the perimeter is 32 cm, so the side length is: \[ a_2 = \frac{32}{4} = 8 \, \text{cm}. \] Step 2: The areas of the squares are: \[ \text{Area of first square} = a_1^2 = 10^2 = 100 \, \text{cm}^2, \] \[ \text{Area of second square} = a_2^2 = 8^2 = 64 \, \text{cm}^2. \] Step 3: The difference in areas is: \[ \text{Difference in areas} = 100 - 64 = 36 \, \text{cm}^2. \] Step 4: Let the side length of the third square be \( a_3 \). The area of the third square is 36 cm\(^2\), so: \[ a_3^2 = 36 \quad \Rightarrow \quad a_3 = 6 \, \text{cm}. \] Step 5: The perimeter of the third square is: \[ P_3 = 4a_3 = 4 \times 6 = 24 \, \text{cm}. \]