SOLUTION: A piece of wire 40 in. long is bent into form of a right triangle, one of whose legs is 15 in. long. Determine the lengths of the other two sides. This one is Mensuration problem.

Question 551393: A piece of wire 40 in. long is bent into form of a right triangle, one of whose legs is 15 in. long. Determine the lengths of the other two sides. This one is Mensuration problem. It's really hard to answer. Someone help me. Please, thank you~ <3
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The wire is 40 inches long. Therefore, we know the perimeter of the triangle it forms is 40 inches.
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One of the two legs is given as being 15 inches long. Therefore, the other leg added to the hypotenuse have to equal the remainder of the 40 inches. So the unknown leg plus the hypotenuse must be 25 inches (the 40 inches minus the 15 inches equals 25 inches). Let H represent the unknown length of the hypotenuse and let L represent the unknown length of one of the legs. Since the hypotenuse plus the unknown leg must add up to 25 inches we can write:
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We can then subtract L from both sides to get:
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Next, let's look at the Pythagorean theorem. It states that the square of the hypotenuse is equal to the sum of the squares of the two legs of a right triangle. In equation form this is:
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We know that one of the legs is 15 inches long. Let's substitute 15 for one of the legs and this makes the Pythagorean equation become:
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Square the 15 to get 225 and the Pythagorean equation that results is:
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Note that we dropped the subscript on the unknown leg just to simplify the notation.
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Recall that we previously found that H = 25 - L. Let's substitute 25 - L for its equal H in the Pythagorean equation to get:
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Square out the left side of this equation to get:
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We can eliminate the two squared L terms by subtracting from both sides of the equation. The resulting simplified equation then becomes:
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Subtract 625 from both sides of this equation to get:
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Solve for the unknown leg L by dividing both sides of this equation by -50 to find that:
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which reduces to:
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So now we know that the two legs of this right triangle are 8 and 15. Since the perimeter of the triangle is to be 40 inches, the hypotenuse must be the length of the wire remaining. So take the 40 inches and subtract 8 and then subtract 15 and you get 17 inches that is left for the length of the hypotenuse.
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Just to give us some confidence in this answer, return to the Pythagorean equation and substitute these values to ensure that they work for this right triangle.
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Square each of the terms to get:
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If we add the two terms on the right, we do get:
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So our answer checks. The right triangle is a 8 inch, 15 inch , 17 inch triangle.
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Hope that this explanation helps you to understand how this problem, and others like it, can be solved. Good luck!
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