SOLUTION: The altitude of a triangle is 3 inches more than its base. What are the dimensions if the area of the triangle is 29 square inches?

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Question 111378: The altitude of a triangle is 3 inches more than its base. What are the dimensions if the area of the triangle is 29 square inches?
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
a=b+3
ab/2=A
b(b+3)/2=29
2b(b+3)/2=29*2
b(b+3)=58
b^2+3b=58
b^2+3b-58=58-58
b^2+3b-58=0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-58+=+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=%283%29%5E2-4%2A1%2A-58=241.

Discriminant d=241 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+241+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+241+%29%29%2F2%5C1+=+6.26208734813001
x%5B2%5D+=+%28-%283%29-sqrt%28+241+%29%29%2F2%5C1+=+-9.26208734813001

Quadratic expression 1x%5E2%2B3x%2B-58 can be factored:
1x%5E2%2B3x%2B-58+=+%28x-6.26208734813001%29%2A%28x--9.26208734813001%29
Again, the answer is: 6.26208734813001, -9.26208734813001. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-58+%29

b=6.262...
a=9.262...
Check:
6.262*9.262/2=29 approx.