SOLUTION: the base of a triangle is 5cm greater than the height. The area is 52^2. Find the height and the lenth of the base.

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Question 439695: the base of a triangle is 5cm greater than the height. The area is 52^2. Find the height and the lenth of the base.
Answer by asuar010(338) About Me  (Show Source):
You can put this solution on YOUR website!
first assign values to the base and the height of the triangle:
h=x
b=x+5
the formula of the area of a triangle is A=(1/2)b*h... so by substituting the values we get 52%5E2=%281%2F2%29%28x%2B5%29%2Ax and simplifying this formula we get x%5E2%2B5x=2%2852%5E2%29 which becomes x%5E2%2B5x-5408=0 then
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B5x%2B-5408+=+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-5408=21657.

Discriminant d=21657 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+21657+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+21657+%29%29%2F2%5C1+=+71.0815873707546
x%5B2%5D+=+%28-%285%29-sqrt%28+21657+%29%29%2F2%5C1+=+-76.0815873707546

Quadratic expression 1x%5E2%2B5x%2B-5408 can be factored:
1x%5E2%2B5x%2B-5408+=+1%28x-71.0815873707546%29%2A%28x--76.0815873707546%29
Again, the answer is: 71.0815873707546, -76.0815873707546. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-5408+%29

so to get the values of the length and base of the triangle we add 5 to 71.08 so the real values are height=71.08 and base=76.08