The length of a rectangle is 12 centimeters less than its width. What are the dimensions of the rectangle if it’s area is 85 square centimeters?

Guest Feb 13, 2020

#1**+2 **

Let the width = W

Let the length, L = W - 12

Area = W * L

So.....

85 = W ( W - 12) simplify

85 = W^2 - 12W rearrange as

W^2 -12W - 85 = 0 factor

(W+ 5) (W -17) = 0

Setting both factors to 0 and solving for W produces

W = - 5 (reject)

W = 17 (accept)

And L = W - 12 = 17 - 12 = 5

CPhill Feb 13, 2020

#2**+1 **

Let's make "x" the width.

Length = x-12.

Area of rectangle: Width * Length.

This means: x(x-12) = 85.

Simplifying that is: x^2 - 12x = 85.

Rearranging it: x^2 - 12x - 85 = 0.

Factor it: (x+5)(x+17)-85 = 0

We can set both factors to 0 and solve for x:

x = -5 which doesn't work

**x = 17 which works.**

And for the Length: **x**** - 12 = 17 -12 = 5.**

I used the same method as CPhill though...

AnimalMaster Feb 13, 2020