SOLUTION: The area of a rectangle is 66m^2, and the length of the rectangle is 7m less than three times the width. Find the dimesions of the rectangle?

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Question 921124: The area of a rectangle is 66m^2, and the length of the rectangle is 7m less than three times the width. Find the dimesions of the rectangle?
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
area = 66 m^2
let x,y be the length and width of rectangle
as per the data x = 3*y-7
But area X*Y =66 m^2
substitute x= 3y-7 in above equation
(3y-7)*y = 66
3y*y-7*y =66
3y^2 -7y=66
subtract 66 on both sides
3y^2 -7y-66 =66-66
3y^2-7y -66 =0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 3y%5E2%2B-7y%2B-66+=+0) has the following solutons:

y%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=%28-7%29%5E2-4%2A3%2A-66=841.

Discriminant d=841 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--7%2B-sqrt%28+841+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-7%29%2Bsqrt%28+841+%29%29%2F2%5C3+=+6
y%5B2%5D+=+%28-%28-7%29-sqrt%28+841+%29%29%2F2%5C3+=+-3.66666666666667

Quadratic expression 3y%5E2%2B-7y%2B-66 can be factored:
3y%5E2%2B-7y%2B-66+=+3%28y-6%29%2A%28y--3.66666666666667%29
Again, the answer is: 6, -3.66666666666667. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-7%2Ax%2B-66+%29

But Y cannot be negative
hence y =6
x= 3*6-7
=18-7
=11
length = 11 m
width = 6 m