SOLUTION: The longer leg of a right triangle measures 2 feet more than twice the length of the shorter leg. The hypotenuse measures 3 feet more than twice the shorter leg. Find the length

Question 200264: The longer leg of a right triangle measures 2 feet more than twice the length of the shorter leg. The hypotenuse measures 3 feet more than twice the shorter leg. Find the length of all 3 sides.
3+2n=2+2n+n-I am not sure if this is correct or not.
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
a^2+b^2=c^2 is the formula for a right triangle given the three sides.
x^2+(2x+2)^2=(2x+3)^2
x^2+4x^2+8x+4=4x^2+12x+9
x^2+8x-12x+4-9=0
x^2-4x-5=0
(x-5)(x+1)=0
x-5=0
x=5 ft. ans. for the shorter leg.
2*5+2=10+2=12 ft. ans. for the longer leg.
2*5+3=10+3=13 ft. ans. for the hypotenuse.
Proof:
5^2+12^2=13^2
25+144=169
169=169

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