SOLUTION: The base of a triangular sail is 5m shorter than its height. The area is 18m^2. Find the base and the height of the sail.

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Question 129879: The base of a triangular sail is 5m shorter than its height. The area is 18m^2. Find the base and the height of the sail.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=height

Since the "base of a triangular sail is 5m shorter than its height", we have the equality b=x-5

A=%28b%2Ah%29%2F2 Start with the formula for the area of a triangle


18=%28%28x-5%29%2Ax%29%2F2 Plug in b=x-5, h=x, and A=18


36=%28x-5%29%2Ax Multiply both sides by 2


36=x%5E2-5x Distribute


0=x%5E2-5x-36 Subtract 36 from both sides



0=%28x-9%29%28x%2B4%29 Factor the right side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
x-9=0 or x%2B4=0

x=9 or x=-4 Now solve for x in each case


So our possible answers are
x=9 or x=-4


However, since a negative height doesn't make sense, our only solution is x=9



So the height is 9 m

Now subtract 5 from the height to get the base


b=9-5=4


So the base is 4 m



Check:


A=%28b%2Ah%29%2F2 Start with the formula for the area of a triangle


18=%284%2A9%29%2F2 Plug in b=4, h=9, and A=18


18=36%2F2 Multiply


18=18 Divide. Since the two sides of the equation are equal, this verifies our answer.