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.

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) (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

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.

RELATED QUESTIONS
The base of a triangular sail is 15 meters shorter than its height.The area is 92m^2.... (answered by Cromlix)

The base of a triangular sail is 15m shorter than its height.The area is 92m^2. Find the... (answered by sudhanshu_kmr)

The base of a triangular sail is 16 m shorter than its height. The area is 130m squared.... (answered by Cromlix)

The base of a triangular sail is 19 m shorter than its height. The area is 145 m... (answered by jorel555)

The base of a triangular sail is 14 m shorter than its height. The area is 88 m squared . (answered by ikleyn)

The base of a triangular sail is 6m shorter than the height.The area is 20 m^2.Find the... (answered by MathLover1)

the base of a triangular sail is 20m shorter than it's height. the area is 150m2. find... (answered by unlockmath)

The base of a triangular sail is 14 m shorter than its height. The area is 120 m^2.... (answered by imapoet_2003)

Hi, I am needing a little help with this algebra.... The base of a triangular sail... (answered by nerdybill)