Question

If a rectangle has an area of 2x^2+7x+3 find the perimeter

Answer 1

Perimeter of a rectangle = 6x + 8

Solution:

Given area of a rectangle = $2x^2+7x+3$

Let us first factor the given polynomial.

$2x^2+7x+3=2x^2+x+6x+3$

                    $=(2x^2+x)+(6x+3)$

Taking out common terms in the above expression

                    $=x(2x+1)+3(2x+1)$

Taking out common term $2x+1$ in the above expression

                    $=(2x+1)(x+3)$

$2x^2+7x+3=(2x+1)(x+3)$

Area of a rectangle = l × b

Therefore, $l=2x+1$ and $b=x+3$

Perimeter of a rectangle = 2(l + b)

                                         $=2[(2x+1)+(x+3)]$

                                         $=2(2x+1+x+3)$

                                         $=2(3x+4)$

                                         $=6x+8$

The answer is same if you take l = x + 3 and b = 2x + 1.

Hence, perimeter of a rectangle = 6x + 8.