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Question 112425This question is from textbook Introductory Algebra
: A lot is in the shape of a right triangle. The shorter leg measures 120 meters. The hypotenuse is 40 meters longer than the length of the longer leg. How long is the longer leg?
This question is from textbook Introductory Algebra
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Since the question asks for the length of the longer leg, let's use x to denote this length.
We are told that the hypotenuse of the triangle is 40 meters longer than the longer leg, so the hypotenuse must be x + 40.
Pythagoras tells us that in any right triangle with legs a and b and hypotenuse c, the following is true:
 .
In our problem, a = 120 meters, b = x meters, and c = x + 40 meters. Therefore:
 , so the longer leg is 160 meters. And, by the way, the hypotenuse must be 200 meters (160 + 40)
Does this answer make sense?
First, x is supposed to be the longer leg, and 160 is larger than 120. It is also 40 meters smaller than the 200 meter hypotenuse.
Also, 120:160:200 reduces to 3:4:5, and we know that a 3, 4, 5 triangle is a right triangle.
Hope this helps.
John
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