SOLUTION: The hypotenuse of a triangle is 17 cm. The length of one leg is 1 cm less than twice the length of the other. Find the length of each leg.

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Question 823533: The hypotenuse of a triangle is 17 cm. The length of one leg is 1 cm less than twice the length of the other. Find the length of each leg.
Found 2 solutions by ewatrrr, TimothyLamb:
Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi
The hypotenuse of a triangle is 17 cm.
The length of one leg is 1 cm less than twice the length of the other.
Find the length of each leg: and
Applying the Pythagorean Theorem
x^2 + (2x-1)^2 = 17^2 =289
x^2 + 4x^2 - 4x + 1 = 289
5x^2 - 4x - 288 = 0

x = -7.5, 8 (tossing out negative solution for unit measure
x = 8cm and the other leg is 15cm
CHECKING our answer***
64 + 225 = 289

Answer by TimothyLamb(4379) (Show Source):
You can put this solution on YOUR website!
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a = x
b = 2x - 1
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17 = sqrt( (2x - 1)(2x - 1) + xx )
289 = (2x - 1)(2x - 1) + xx
289 = 4xx - 4x + 1 + xx
5xx - 4x - 288 = 0
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the above quadratic equation is in standard form, with a=5, b=-4, and c=-290
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
5 -4 -288
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two real roots (the x-intercepts), which are:
x = 8
x = -7.2
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negative length doesn't make sense for this problem, so use the positive root
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answer:
a = 8 cm
b = 15 cm
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