SOLUTION: The length of a rectangle is 1ft less than 3 times the width. There is 310 ft squared.Find the dimension of the rectangle.

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Question 282287: The length of a rectangle is 1ft less than 3 times the width. There is 310 ft squared.Find the dimension of the rectangle.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
l=3w-1
A=lw
A=310
310=lw
310=(3w-1)w
310=3w^2-w
0=3w%5E2-w-310
w=10.33333 or 31/3 ft so l=3(31/3)-1=30ft
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 3w%5E2%2B-1w%2B-310+=+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=%28-1%29%5E2-4%2A3%2A-310=3721.

Discriminant d=3721 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+3721+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+3721+%29%29%2F2%5C3+=+10.3333333333333
w%5B2%5D+=+%28-%28-1%29-sqrt%28+3721+%29%29%2F2%5C3+=+-10

Quadratic expression 3w%5E2%2B-1w%2B-310 can be factored:
3w%5E2%2B-1w%2B-310+=+3%28w-10.3333333333333%29%2A%28w--10%29
Again, the answer is: 10.3333333333333, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-1%2Ax%2B-310+%29