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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Let x=height

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

Start with the formula for the area of a triangle


Plug in , , and


Multiply both sides by 2


Distribute


Subtract 36 from both sides



Factor the right side (note: if you need help with factoring, check out this solver)



Now set each factor equal to zero:
or

or Now solve for x in each case


So our possible answers are
or


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



So the height is 9 m

Now subtract 5 from the height to get the base





So the base is 4 m



Check:


Start with the formula for the area of a triangle


Plug in , , and


Multiply


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