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.
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~ :)