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 square.

• A. $8$ cm, $12$ cm
• B. $12$ cm, $15$ cm
• C. $6$ cm, $10$ cm
• D. $16$ cm, $20$ cm

Answer 1

The correct option is D $16$ cm, $20$ cm

Applying the above condition, we get
$x^2+(x+4{)}^2=656$
$2x^2+8x+16=656$
$2x^2+8x-640=0$
$x^2+4x-320=0$
$(x+2{)}^2=324$
$(x+2{)}^2={18}^2$
Now length cannot be negative, hence
$x+2=18$
$x=16$ cm
Hence, $(x+4)=20$ cm.