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: $$P_3 = 4a_3 = 4 \times 6 = 24 \, \text{cm}.$$