SOLUTION: The hypotenuse of a given right triangle is 6 cm longer than the shorter leg. The length of the shorter leg is 2 cm less than that of the longer leg. Find the length of the three

Algebra ->  Triangles -> SOLUTION: The hypotenuse of a given right triangle is 6 cm longer than the shorter leg. The length of the shorter leg is 2 cm less than that of the longer leg. Find the length of the three      Log On


   

Question 280687: The hypotenuse of a given right triangle is 6 cm longer than the
shorter leg. The length of the shorter leg is 2 cm less than that of the longer
leg. Find the length of the three sides
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
A^2+B^2=C^2
A=X
B=X+2
C=X+6
X^2+(X+2)^2=(X+6)^2
X^2+X^2+4X+4=X^2+12X+36
2X^2-X^2+4X-12X+4-36=0
X^2-8X-32=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
X=(8+-SQRT[-8^2-4*1*-32])/2*1
X=(8+-SQRT[64+128])/2
X=(8+-SQRT192)/2
X=(8+-13.8564)/2
X=(8+13.8564)/2
X=21.8564/2
X=10.9282 ANS FOR THE SHORT SIDE.
10.9282+2=12.9282 FOR THE LONG SIDE.
10.9282+6=16.9282 FOR THE HYPOTENUSE.
PROOF:
10.9282^2+12.9282^2=16.9282^2
119.4256+167.13835=286.56395
286.56395=286.56395