SOLUTION: the base of a triangle is four more than twice its heights. if the area of the triangle is 45 square centimeters, find its base and height

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Question 918851: the base of a triangle is four more than twice its heights. if the area of the triangle is 45 square centimeters, find its base and height
Answer by asuar010(338) About Me  (Show Source):
You can put this solution on YOUR website!
first rewrite that b=2h+4 the write the formula for Area which is A=%28b%2Ah%29%2F2 then substitute and you get A=h%282h%2B4%29%2F2 then substitute 45=h%282h%2B4%29%2F2 then 90=2h%5E2%2B4h then 0=2h%5E2%2B4h-90 then
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B4x%2B-90+=+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=%284%29%5E2-4%2A2%2A-90=736.

Discriminant d=736 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+736+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+736+%29%29%2F2%5C2+=+5.78232998312527
x%5B2%5D+=+%28-%284%29-sqrt%28+736+%29%29%2F2%5C2+=+-7.78232998312527

Quadratic expression 2x%5E2%2B4x%2B-90 can be factored:
2x%5E2%2B4x%2B-90+=+2%28x-5.78232998312527%29%2A%28x--7.78232998312527%29
Again, the answer is: 5.78232998312527, -7.78232998312527. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-90+%29
and then we only use the positive solution