SOLUTION: Solve using quadratic formula. The diagonal of a rectangle is 15m long and one side is 2m longer than the other. Find the dimensions of the rectangle. Please HELP

Algebra ->  Rectangles -> SOLUTION: Solve using quadratic formula. The diagonal of a rectangle is 15m long and one side is 2m longer than the other. Find the dimensions of the rectangle. Please HELP      Log On


   

Question 828010: Solve using quadratic formula.
The diagonal of a rectangle is 15m long and one side is 2m longer than the other. Find the dimensions of the rectangle.
Please HELP
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonal of a rectangle is 15m long and one side is 2m longer than the other.
.
Let w = width
then
w+2 = length
.
applying Pythagorean's theorem:
w^2 + (w+2)^2 = 15
w^2 + (w+2)(w+2) = 15
w^2 + w^2+4w+4 = 15
2w^2+4w+4 = 15
2w^2+4w-11 = 0
applying the quadratic formula we get:
w = 1.55 m (width)
.
Length:
w+2 = 1.55+2 = 3.55 m (length)
.
Dimensions are:
1.55m by 3.55 m
.
Details of quadratic formula:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 2w%5E2%2B4w%2B-11+=+0) has the following solutons:

w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%284%29%5E2-4%2A2%2A-11=104.

Discriminant d=104 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+104+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%284%29%2Bsqrt%28+104+%29%29%2F2%5C2+=+1.54950975679639
w%5B2%5D+=+%28-%284%29-sqrt%28+104+%29%29%2F2%5C2+=+-3.54950975679639

Quadratic expression 2w%5E2%2B4w%2B-11 can be factored:
2w%5E2%2B4w%2B-11+=+2%28w-1.54950975679639%29%2A%28w--3.54950975679639%29
Again, the answer is: 1.54950975679639, -3.54950975679639. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-11+%29