SOLUTION: the base of a triangle exceeds twice its altitude by 18m. If the area of the triangle be360 sq.m . What is its altitude?

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Question 957519: the base of a triangle exceeds twice its altitude by 18m. If the area of the triangle be360 sq.m . What is its altitude?
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
A=area=360 sq m; h=altitude; b=base=2h+18m
A=%281%2F2%29bh Substitute for b.
360m%5E2=%281%2F2%29%282h%2B18%29%28h%29 Multiply each side by 2.
720m%5E2=2h%5E2%2B18h Subtract 720 m^2 from each side
0=2h%5E2%2B18h-720m%5E2
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ah%5E2%2Bbh%2Bc=0 (in our case 2h%5E2%2B18h%2B-720+=+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=%2818%29%5E2-4%2A2%2A-720=6084.

Discriminant d=6084 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+6084+%29%29%2F2%5Ca.

h%5B1%5D+=+%28-%2818%29%2Bsqrt%28+6084+%29%29%2F2%5C2+=+15
h%5B2%5D+=+%28-%2818%29-sqrt%28+6084+%29%29%2F2%5C2+=+-24

Quadratic expression 2h%5E2%2B18h%2B-720 can be factored:
2h%5E2%2B18h%2B-720+=+2%28h-15%29%2A%28h--24%29
Again, the answer is: 15, -24. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B18%2Ax%2B-720+%29

h=15m ANSWER: The altitude of the triangle is 15 meters.
CHECK:
b=2h+18m=2(15m)+18m=48m The base of the triangle is 48 meters.
A=1/2bh
360sq m=1/2(48m)(15m)
360 sq m=360 sq m