Problema Solution
The length of the shortest side of a right triangle is 8 inches. The lengths of the other two sides are represented by consecutive odd integers. Which equation could be used to find the lengths of the other sides of the triangle?
Answer provided by our tutors
Two consecutive odd integers can be written as:
2x - 1 and 2x + 1, where x is integer and 2x - 1 > 0, x > 1/2
The larger odd number 2x + 1 is the length of the hypotenuse while the smaller 2x - 1 is the length of the side.
Using the Pythagorean Theorem we have have the equation that we will use to find the other sides of the triangle:
8^2 + (2x - 1)^2 = (2x + 1)^2
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click here to see the equation solved for x
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x = 8
2x - 1 = 2*8 - 1 = 15 in
2x + 1 = 17 in
The other sides of the right triangle are: the hypotenuse is 17 in and the other side is 15 in.