Question

Two squares have sides x cm and (x + 5) cm. The sum of their areas is 697 square cm.
Express this as an algebraic equation in x.

Answer 1

Given that, sides of two squares are $xcm$ and $(x+5)cm$ respectively.

Also, sum of their areas is $697c{m}^2$.

We know that, area of a square $=side\times side$

$\therefore$ Area of the square with side $x$ $=x^{2}c{m}^2$

and area of the square with side $(x+5)=(x+5{)}^{2}c{m}^2$

According to the question:

$x^2+(x+5{)}^2=697$

We know that, $(a+b{)}^2=a^2+2ab+b^2$

$\therefore (x+5{)}^2=x^2+10x+25$

$\Rightarrow x^2+x^2+10x+25=697$

$\Rightarrow 2x^2+10x+25-697=0$

$\Rightarrow 2x^2+10x-672=0$

$\therefore x^2+5x-336=0$

Hence, the required algebraic equation in $x$ is $x^2+5x-336=0$.