Question

Sum of the areas of two squares is 468 m${}^2$. If the difference of their perimeters is 24 m, formulate the quadratic equation to find the sides of the two squares.

Answer 1

Let the length of each side of a square be x metres.

Then, Perimeter $=4x$

Therefore,

Perimeter of second square $=24+4x=4(6+x)$ metres

Length of each side of second square $=6+x$ metres

According to question,

$x^2+(6+x{)}^2=468$

$x^2+(36+12x+x^2)=468$

$2x^2+12x-432=0$

$x^2+6x-216=0$

This is the required equation.