SOLUTION: Please someone helps me answer this. The face of the triangular concrete panel has an area of 7 square meters, and its base of 3 meters longer than twice its height.Find the length

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Question 949471: Please someone helps me answer this. The face of the triangular concrete panel has an area of 7 square meters, and its base of 3 meters longer than twice its height.Find the length of the base.
Answer by macston(5194) About Me  (Show Source):
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Please someone helps me answer this. The face of the triangular concrete panel has an area of 7 square meters, and its base of 3 meters longer than twice its height.Find the length of the base.
A=%281%2F2%29bh
7+sq+m=%281%2F2%29%282h%2B3%29%28h%29
7+sq+m=%28h%2B1.5%29%28h%29
7+sq+m=h%5E2%2B1.5h
0=h%5E2%2B1.5h-7sq+m
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ah%5E2%2Bbh%2Bc=0 (in our case 1h%5E2%2B1.5h%2B-7+=+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=%281.5%29%5E2-4%2A1%2A-7=30.25.

Discriminant d=30.25 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1.5%2B-sqrt%28+30.25+%29%29%2F2%5Ca.

h%5B1%5D+=+%28-%281.5%29%2Bsqrt%28+30.25+%29%29%2F2%5C1+=+2
h%5B2%5D+=+%28-%281.5%29-sqrt%28+30.25+%29%29%2F2%5C1+=+-3.5

Quadratic expression 1h%5E2%2B1.5h%2B-7 can be factored:
1h%5E2%2B1.5h%2B-7+=+1%28h-2%29%2A%28h--3.5%29
Again, the answer is: 2, -3.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1.5%2Ax%2B-7+%29

h=2 Height is 2 meters
A=(1/2)bh
7 sq meters=1/2b(2 meters)
7 sq meters=b(1 meter) To keep units correct, divide each side by 1 meter
7 meters=b ANSWER: Base is 7 feet.
CHECK
Base=2h+3
7 meters=2(2 meters)+3 meters
7 meters=7meters
Area=1/2bh
7 sq m=1/2(7 feet)(2 feet)=1/2(14 sq ft)=7 sq m