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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Solve and graph linear equations:

https://sooeet.com/math/linear-equation-solver.php

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Solve quadratic equations, quadratic formula:

https://sooeet.com/math/quadratic-formula-solver.php

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Solve systems of linear equations up to 6-equations 6-variables:

https://sooeet.com/math/system-of-linear-equations-solver.php 

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