SOLUTION: The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is

Algebra ->  Rectangles -> SOLUTION: The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is       Log On


   

Question 945217: The width and the length of a rectangle are consecutive even integers. If the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. What is the area of the original rectangle?


12 square inches
48 square inches
96 square inches

Help, pleaseee?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
Width=W; Length =L=W+2
(W-3)(W+2)=24 in sq
W^2-W-6=24
W^2-W-30=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-1x%2B-30+=+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=%28-1%29%5E2-4%2A1%2A-30=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+121+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%28-1%29-sqrt%28+121+%29%29%2F2%5C1+=+-5

Quadratic expression 1x%5E2%2B-1x%2B-30 can be factored:
1x%5E2%2B-1x%2B-30+=+1%28x-6%29%2A%28x--5%29
Again, the answer is: 6, -5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-1%2Ax%2B-30+%29

Answers: 6,-5 Since answer must be even:
The width is 6
L=W+2=6+2-8
The length is 8
Area = L * W = 6*8=48
ANSWER The area of the original rectangle was 48 sq in