SOLUTION: The length of a rectangular flower bed is 11 feet less than 3 times its width. The area of the bed is 20 ft^2. Find the dimensions of the flower bed.

Algebra ->  Surface-area -> SOLUTION: The length of a rectangular flower bed is 11 feet less than 3 times its width. The area of the bed is 20 ft^2. Find the dimensions of the flower bed.       Log On


   

Question 630170: The length of a rectangular flower bed is 11 feet less than 3 times its width. The area of the bed is 20 ft^2. Find the dimensions of the flower bed.
Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
Let w be the width of the rectangle then the length is 3w-11. For the area we have that +%28w%29%283%2Aw-11%29=20+. +3%2Aw%5E2-11%2Aw-20=0+
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B-11x%2B-20+=+0) has the following solutons:

x%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=%28-11%29%5E2-4%2A3%2A-20=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--11%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-11%29%2Bsqrt%28+361+%29%29%2F2%5C3+=+5
x%5B2%5D+=+%28-%28-11%29-sqrt%28+361+%29%29%2F2%5C3+=+-1.33333333333333

Quadratic expression 3x%5E2%2B-11x%2B-20 can be factored:
3x%5E2%2B-11x%2B-20+=+3%28x-5%29%2A%28x--1.33333333333333%29
Again, the answer is: 5, -1.33333333333333. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B-11%2Ax%2B-20+%29
. The width is 5 ft and the length is 3*5-11=4