SOLUTION: Problem: The mainsail on a sailboat is a right triangle in which the hypotenuse is called the leech. A 12-foot tall mainsail has a leech of 13 feet. If sailcloth costs $10.00 pe

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Problem: The mainsail on a sailboat is a right triangle in which the hypotenuse is called the leech. A 12-foot tall mainsail has a leech of 13 feet. If sailcloth costs $10.00 pe      Log On

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Question 145017: Problem: The mainsail on a sailboat is a right triangle in which the hypotenuse is called the leech. A 12-foot tall mainsail has a leech of 13 feet. If sailcloth costs $10.00 per square foot, what is the cost of a new mainsail?

Answer by nerdybill(5412) About Me  (Show Source):
You can put this solution on YOUR website!
To answer this question, you need to know the "area" of the sail. The area of any triangle is 1/2(base)(height).
The key is that they told you that it is a "right-triangle". Knowing that, you can apply Pythagorean's theorem to find the length of the base of the sail.

Let x = length of the base of the sail
then
x^2 + 12^2 = 13^2
x^2 + 144 = 169
x^2 = 25
x = 5 feet
Area of sail:
1/2(base)(height)
= 1/2(5)(12)
= 5(6)
= 30 sq ft
At $10 per sq ft then the total cost is:
10 * 30 = $300