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:
[tex]A=x^2+14x+24[/tex]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:
[tex]x^2+14x+24=(x+2)(x+12)[/tex]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
