SOLUTION: In a right triangle , the shorter leg is 6 less than the longer leg. The hypotenuse is 6 less than twice the shorter leg. Set up a quadratic equation and use it to determine the le

Question 128813: In a right triangle , the shorter leg is 6 less than the longer leg. The hypotenuse is 6 less than twice the shorter leg. Set up a quadratic equation and use it to determine the lenghth of the hypotenuse of the right triangle.
Found 2 solutions by checkley71, edjones:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
X^2+(X-6)^2=[2(X-6)-6]^2
X^2+X^2-12X+36=[2X-12-6]^2
2X^2-12X+36=(2X-18)^2
2X^2-12X+36=4X^2-72X+324
2X^2-4X^2-12X+72X+36-324=0
-2X^2+60X-288=0
-2(X^2-30X+144)=0
-2(X-6)(X-24)=0
X-24=0
X=24 ANSWER FOR THE LONGER LEG.
24-6=18 IS FOR THE SHORTER LEG
18^2+24^2=H^2
324+576=H^2
H^2=900
H=SQRT900
H=30 FOR THE HYPOTENUSE.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let a=longer leg, b=shorter leg, c=hypotenuse
b=a-6
c=2b-6=2(a-6)-6=2a-12-6=2a-18
a^2+b^2=c^2
a^2+(a-6)^2=(2a-18)^2
a^2+a^2-12a+36=4a^2-72a+324
2a^2-60a+288=0
(a-6)(a-24)=0
a=6 not an answer in this problem.
a=24
c=2a-18
=48-18
=30 Ans.
.
Ed

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