SOLUTION: The area of a triangle is 140 square feet.If the height is 7 more than the base, find the length of the height and base of the triangle.

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Question 950228: The area of a triangle is 140 square feet.If the height is 7 more than the base, find the length of the height and base of the triangle.

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a triangle is 140 square feet.If the height is 7 more than the base, find the length of the height and base of the triangle.
b=base; h=heught=b+7; a=1/2bh
a=1/2bh
140+sq+ft=1%2F2bh Multiply each side by 2.
280+sq+ft=bh Substitute for h
280+sq+ft=b%28b%2B7%29
280+sq+ft=b%5E2%2B7b Subtract 280 sq ft from each side
0=b%5E2%2B7b-280+sq+ft
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ab%5E2%2Bbb%2Bc=0 (in our case 1b%5E2%2B7b%2B-280+=+0) has the following solutons:

b%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=%287%29%5E2-4%2A1%2A-280=1169.

Discriminant d=1169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+1169+%29%29%2F2%5Ca.

b%5B1%5D+=+%28-%287%29%2Bsqrt%28+1169+%29%29%2F2%5C1+=+13.5953209972788
b%5B2%5D+=+%28-%287%29-sqrt%28+1169+%29%29%2F2%5C1+=+-20.5953209972788

Quadratic expression 1b%5E2%2B7b%2B-280 can be factored:
1b%5E2%2B7b%2B-280+=+1%28b-13.5953209972788%29%2A%28b--20.5953209972788%29
Again, the answer is: 13.5953209972788, -20.5953209972788. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-280+%29

b=13.595 feet
h=b+7=13.595+7=20.595
CHECK:
a=1/2bh
280 sq ft=1/2(13.595)(20.595)
280 sq ft=280 sq ft