Question

16. The area of the rectangle is x^2+14x+24.Find the length and width (the factors),then determine the perimeter of the rectangle.Length:Width:Perimeter:

Answer 1

Given a rectangle of width W and length L, the area is calculated by:

A = W.L

The perimeter of the rectangle is:

P = 2(W + L)

We are given the area of a rectangle with the equation:

`A=x^2+14x+24`

To find the dimensions of the rectangle, we must factor the polynomial.

It's easily done by inspection: find two numbers that added result in 14 and multiplied result in 24. Those numbers are 12 and 2, thus:

`x^2+14x+24=(x+2)(x+12)`

The factors are the width and the length of the rectangle (the width smaller than the length), thus:

Width = x+2

Length = x + 12

Now calculate the perimeter:

P = 2( x + 2 + x + 12)

P = 2( 2x + 14)

Perimeter = 4x + 28