Question

A rectangle is to be constructed with perimeter $70$ centimeter and area $300$ square centimeters. What should be the length of its sides?

Answer 1

Perimeter of rectangle$=2(l+b)=70cm$
$\Rightarrow$ $l+b=35cm$
$\Rightarrow$ $l=35-b$
Area of rectangle $=l\times b=300sq.cm$
$\Rightarrow$ $(35-b)b=300$
$\Rightarrow$ $b^2-35b+300=0$
$\Rightarrow b^2-20b-15b-300=0$
$\Rightarrow b(b-20)-15(b-20)=0$
$\Rightarrow (b-20)(b-15)=0$
$\Rightarrow b-20$ or $b=15$
$\Rightarrow l=15$ or $20$
Thus, length of sides of rectangle is $15cm$ and $20cm$.