Question

The difference of area of two squares is A. The difference of their perimeters is p. Then the sum of their perimeters is ______ .

• A. 2A/p
• B. 4A/p
• C. 8A/p
• D. 16A/p

Answer 1

The correct option is D

16A/p

$x^2$ – $y^2$ = A

$\Rightarrow$ (x-y)(x+y) = A

$\Rightarrow$ 4(x-y)(x+y) = 4A

$\Rightarrow$ x+y = 4 $\frac{A}{p}$

$\Rightarrow$Sum of perimeters = 4(x + y) = 4($\frac{A}{p}$) = $\frac{16A}{p}$