SOLUTION: one leg of of a right triangle is 2 meters longer than the other leg. The hypotenuse is 2 meters less than twice the length of the shorter leg. Find the length of the shorter leg.

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Question 865116: one leg of of a right triangle is 2 meters longer than the other leg. The hypotenuse is 2 meters less than twice the length of the shorter leg. Find the length of the shorter leg.
Answer by dkppathak(439) About Me  (Show Source):
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one leg of of a right triangle is 2 meters longer than the other leg. The hypotenuse is 2 meters less than twice the length of the shorter leg. Find the length of the shorter leg.
Answer
let smaller leg is x meter
length of other leg will be X+2 ( as per given conditions)
length of hypotenuse will be 2x-2(as per given conditions )
by Pythagoras theorem of right anle triangle
we know
H^2=smaller leg^2+other Leg^2
(2x-2)^2= X^2+ (X+2)^2
4x^2+4-8x =x^2+x^2+4+4x
4x^2+4-8x =2x^2+4+4x
4x^2+4-8x - 2x^2 -4-4x = 0
2x^2-12x=0
2x(x-6)=0
therefor
2x=0 or x-6=0
x=0 or x=6
neglecting x=0
therefore x=6 meter
hypotenuse will be 2x-2=2x6-2=10 meter
other leg will be x+2 = 8 meter
Answer
smaller leg =6 meters
other leg =8 meters
hypotenuse =10 meters
A