SOLUTION: The length of a rectangular yard is 5 feet longer than its width, x. The area of the yard is 104 sq ft. Use a quadratic to solve for the width.

Algebra ->  Rectangles -> SOLUTION: The length of a rectangular yard is 5 feet longer than its width, x. The area of the yard is 104 sq ft. Use a quadratic to solve for the width.       Log On


   

Question 945545: The length of a rectangular yard is 5 feet longer than its width, x. The area of the yard is 104 sq ft. Use a quadratic to solve for the width.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
(X+5)(X)=104 sq ft
X%5E2%2B5X=104sqft Subtract 104 from each side
X%5E2%2B5X-104=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-104+=+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=%285%29%5E2-4%2A1%2A-104=441.

Discriminant d=441 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+441+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+441+%29%29%2F2%5C1+=+8
x%5B2%5D+=+%28-%285%29-sqrt%28+441+%29%29%2F2%5C1+=+-13

Quadratic expression 1x%5E2%2B5x%2B-104 can be factored:
1x%5E2%2B5x%2B-104+=+1%28x-8%29%2A%28x--13%29
Again, the answer is: 8, -13. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-104+%29

answers are 8,-13
ANSWER the width of the yard is 8 feet,
CHECK:
length = W+5=8+5=13 ft
Area=104 sq ft
104 sq ft=(13ft)(8ft)
104 sq ft=104 sq ft