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.

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Use pythagorean theorem
Call the shorter leg x
The longer leg is 2x+-+3
hypotenuse is 18 cm
x%5E2+%2B+%282x+-+3%29%5E2+=+18%5E2
x%5E2+%2B+4x%5E2+-+12x+%2B+9+=+324
5x%5E2+-+12x+-+315+=+0
use quadratic equation to solve
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
When equation is in the form ax%5E2+%2B+bx+%2B+c+=+0
a+=+5
b+=+-12
c+=+-315
x+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A5%2A%28-315%29%29%29%2F%282%2A5%29+
x+=+%28+12+%2B-+sqrt%28+144+%2B+6300%29%29%2F+10+
x+=+%28+12+%2B-+sqrt%28+6444%29%29%2F+10+
x+=+%28+12+%2B-+80.275%29+%2F+10
x+=+92.275+%2F+10
x+=+9.23
check answer
The longer leg is 2x+-+3
2%2A9.23+-+3+=+15.46
9.23%5E2+%2B+15.46%5E2+=+18%5E2
85.19+%2B+239+=+324
324.19+=+324
obviously, I'm off a little, but you
get the idea

Answer by checkley71(8403) About Me  (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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
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