SOLUTION: The height of a door is 1.6 feet longer than its width and its front area(neglecting depth) is 1591.4 square feet. Find the width and the height of the door. Find the width of

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Question 436857: The height of a door is 1.6 feet longer than its width and its front area(neglecting depth) is 1591.4 square feet. Find the width and the height of the door.
Find the width of the door in feet
Find the height of the door in feet
(round to one decimal place as needed)
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Area=LxW
x(x+1.6)=1591.4
x2+1.6x=1591.4
Multiply by 10:
10x2+16x-15914=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 10x%5E2%2B16x%2B-15914+=+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=%2816%29%5E2-4%2A10%2A-15914=636816.

Discriminant d=636816 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-16%2B-sqrt%28+636816+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2816%29%2Bsqrt%28+636816+%29%29%2F2%5C10+=+39.1003759380786
x%5B2%5D+=+%28-%2816%29-sqrt%28+636816+%29%29%2F2%5C10+=+-40.7003759380786

Quadratic expression 10x%5E2%2B16x%2B-15914 can be factored:
10x%5E2%2B16x%2B-15914+=+10%28x-39.1003759380786%29%2A%28x--40.7003759380786%29
Again, the answer is: 39.1003759380786, -40.7003759380786. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+10%2Ax%5E2%2B16%2Ax%2B-15914+%29

Throwing out the negative answer, we get the width of the door to be 39.10 ft, and the height to be 40.7 feet. Must be one big a** door.