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

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:

Area of first square:

\[ \text{Area}_1 = a_1^2 = 10^2 = 100 \, \text{cm}^2 \]

Area of second square:

\[ \text{Area}_2 = a_2^2 = 8^2 = 64 \, \text{cm}^2 \]

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 cm², so:

\[ a_3^2 = 36 \quad \Rightarrow \quad a_3 = 6 \, \text{cm} \]

Step 5: The perimeter of the third square is:

\[ P_3 = 4a_3 = 4 \times 6 = 24 \, \text{cm} \]