Question

Two squares have side x cm and (x + 4) cm. The sum of their areas is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.

Answer 1

Given that, two squares have sides x cm and (x + 4) cm.
$Sumoftheirarea=656c{m}^2$
$\therefore x^2+(x+4{)}^2=656$
$x^2+x^2+16+8x=656$
$2x^2+8x–640=0$
$x^2+4x–320=0$
$x^2+20x–16x–320=0$
$x(x+20)–16(x+20)=0$
$(x+20)(x–16)=0$
$x=-20,16$
But, x being side, cannot be negative.
So, x = 16
Thus, the sides of the two squares are 16 cm and 20 cm