Question

Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 $c{m}^2$. Find the sides of the squares.

• A. 12 cm and 16 cm
• B. 16 cm and 20 cm
• C. 10 cm and 14 cm
• D. 6 cm and 10 cm

Answer 1

The correct option is B 16 cm and 20 cm

The area of a square is $sid{e}^{2}sq$. units.
As per the question,
$x^2+(x+4{)}^2=656$
$\Rightarrow x^2+(x^2+8x+16)=656$
$\Rightarrow 2x^2+8x-640=0$
$\Rightarrow x^2+4x-320=0$
$\Rightarrow x^2+20x-16x-320=0$
$\Rightarrow (x+20)(x-16)=0$

Thus, x - 20 or 16.
But the side of a square can't be negative.
$\Rightarrow x=16and(x+4)=20$.

Thus, the sides of the two squares are 16 cm and 20 cm.