Question

Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 sq.cm.
Solve this equation to find the sides of the squares.

Answer 1

The given sides of two squares$=x$cm and $x+4$cm

Sum of their areas$=656$sq.cm

Area of the square$=side\times side$

$\therefore$ Area of the square$=x(x+4)$sq.cm

$\Rightarrow$ Given that sum of the areas is $656$sq.cm

Hence by hypothesis, we have $x(x+4)+x(x+4)=656$

$\Rightarrow 2x(x+4)=656$

$\Rightarrow x^2+4x-328=0$ dividing both sides by $2$

$\Rightarrow x^2+20x-16x-328=0$

$\Rightarrow x(x+20)-16(x+20)=0$

$\Rightarrow (x+20)(x-16)=0$

$\Rightarrow x=-20$ or $x=16$

Case$I:$ If $x=16$

$\Rightarrow x+4=16+4=20$

$\therefore$ The sides of the squares are $16$cm and $20$cm

No negative value is considered as the sides will never be measured negatively.