SOLUTION: A right triangle has sides of length such that the hypotenuse is 3 inches less than twice the shorter leg and the longer leg is 3 inches longer the shorter leg. how long is each si

Algebra ->  Algebra  -> Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A right triangle has sides of length such that the hypotenuse is 3 inches less than twice the shorter leg and the longer leg is 3 inches longer the shorter leg. how long is each si      Log On

Ad: You enter your algebra equation or inequality - Algebrator solves it step-by-step while providing clear explanations. Free on-line demo .
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 378183: A right triangle has sides of length such that the hypotenuse is 3 inches less than twice the shorter leg and the longer leg is 3 inches longer the shorter leg. how long is each side of the triangle?
Answer by ewatrrr(10682) About Me  (Show Source):
You can put this solution on YOUR website!


Hi,

Let x represent the length of the shorter leg.

then the hypotenuse is (2x-3) and the other leg is (x+3)

Applying the Pythagorean Theorem***

x^2  + (x+3)^2 = (2x-3)^2

solving for x

x^2 + x^2 + 6x + 9 = 4x^2 -12x + 9

2x^2 - 18x = 0

2x(x-9)= 0

x = 0 Extraneious solution

x = 9, the length of the shorter leg. Other two sides are 12 & 15

CHECKING our Answer***

81 + 144 = 225