SOLUTION: The area of a tringular sign is 33 squared meters The base of the tringle is 1 meter less than double the altitude. What is the base and height of the triangle

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Question 264673: The area of a tringular sign is 33 squared meters The base of the tringle is 1 meter less than double the altitude. What is the base and height of the triangle
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
Use formula %281%2F2%29b%28h%29=a where b=base h=hieght and a=area
a=33
%281%2F2%29b%28h%29=33
b=2h-1
%281%2F2%29%282h-1%29%28h%29=33
%282%29%281%2F2%29%282h-1%29%28h%29=33%282%29
%282h-1%29%28h%29=66
%282h%5E2-1h%29=66
2h%5E2-1h-66=0 Follow the solver below to get h=(6 or -5)
b=2h-1
b=2%286%29-1
b=11
b=2h-1
b=2%28-5.5%29-1
b=-12
either (b=13)&(h=6) or (b=-12)&(h=-5.5)
.
Checking answers
%281%2F2%29b%28h%29=33
%281%2F2%2911%286%29=33
%281%2F2%29%2866%29=33
.
%281%2F2%29b%28h%29=33
%281%2F2%29-12%28-5.5%29=33
%281%2F2%29%2866%29=33
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ah%5E2%2Bbh%2Bc=0 (in our case 2h%5E2%2B-1h%2B-66+=+0) has the following solutons:

h%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=%28-1%29%5E2-4%2A2%2A-66=529.

Discriminant d=529 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--1%2B-sqrt%28+529+%29%29%2F2%5Ca.

h%5B1%5D+=+%28-%28-1%29%2Bsqrt%28+529+%29%29%2F2%5C2+=+6
h%5B2%5D+=+%28-%28-1%29-sqrt%28+529+%29%29%2F2%5C2+=+-5.5

Quadratic expression 2h%5E2%2B-1h%2B-66 can be factored:
2h%5E2%2B-1h%2B-66+=+2%28h-6%29%2A%28h--5.5%29
Again, the answer is: 6, -5.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-1%2Ax%2B-66+%29