SOLUTION: A garden has the shape of a right triangle with one leg 4 meters longer than the other. The hypotenuse is 4 meters less than twice the length of the shorter leg. What is the length

Question 969743: A garden has the shape of a right triangle with one leg 4 meters longer than the other. The hypotenuse is 4 meters less than twice the length of the shorter leg. What is the length of the shorter leg?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Leg 1 is X meters (all units are meters)
Leg 2 is X+4
Hypotenuse is (2X-4) Twice the length of shorter leg minus 4
Pythagorean Theorem
X^2 + (X+4)^2= (2X-4)^2
X^2 +(X+4)(X+4)=(2X-4)(2X-4)
X^2 + X^2 + 8X +16= 4X^2-16X+16
Move terms to right by subtracting 2 X^2 + 8X +16 from both sides.
0= 2X^2 -24 X The 16s cancel each other.
2X(X-12)=0 Factoring.
X=0 (no sense)
X-12=0 ; X=12
Leg 1 is 12
Leg 2 is 16
Leg 3 is twice Leg 1 (24) - 4=20
This is a 12:16:20 right triangle, 4 times each side of a 3:4:5.

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