SOLUTION: Solve. The longer leg of a right triangle is 3 cm less than twice the shorter leg. The hypotenuse is 18 cm long. Find the length of the shorter leg.

Question 122761: Solve.
The longer leg of a right triangle is 3 cm less than twice the shorter leg. The hypotenuse is 18 cm long. Find the length of the shorter leg.
Found 2 solutions by josmiceli, checkley71:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Use pythagorean theorem
Call the shorter leg
The longer leg is
hypotenuse is cm

use quadratic equation to solve

When equation is in the form

check answer
The longer leg is

obviously, I'm off a little, but you
get the idea
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
X^2+(2X-3)^2=18^2
X^2+4X^2-12X+9=324
5X^2-12X+9-324=0
5X^2-12X-315=0

X=(12+-SQRT[-12^2-4*5*-315])/2*5
X=(12+-SQRT[144+6300])/10
X=(12+-SQRT6444)/10
X=(12+-80.27)/10
X=(12+80.27)/10
X=92.27/10
X=9.227 ANSWER FOR THE SHORTER LEG.
2*9.227-3=18.454-3=15.454 FOR THE LONGER LEG.
PROOF
9.227^2+15.454^2=324
85.138+238.826=324
324~324

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