Posted by **Karina** on Sunday, April 10, 2011 at 11:14pm.

The length of a rectangle is three less than three times the width. The area is 90ft^2. Find the width and the length of the retangle.

- math -
**Jai**, Sunday, April 10, 2011 at 11:37pm
first we represent the unknowns using variables,,

let x = width

let 3x-3 = length (according to the first statement)

now we set up the equation,, since we are given the area, recall that the area of a rectangle is

A = L*W

where L=length and W=width.

substituting,

90 = (3x - 3)(x)

90 = 3x^3 - 3x

0 = 3x^2 - 3x - 90

we can factor out the 3 and just cancel it (since the other side of equation is zero):

0 = 3(x^2 - x - 30)

0 = x^2 - x - 30

since it's factorable,

0 = (x+5)(x-6)

x = -5 and x = 6

since measurements can never be negative, we only take the positive root:

x = 6 ft (width) ; and

3x-3 = 15 ft (length)

hope this helps~ :)

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