SOLUTION: A lot has the shape of a right triangle with one leg 2m longer than the other. The hypotenuse is 2m less than twice the length of the shorter leg. Finf the length of the shorter le

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Question 333647: A lot has the shape of a right triangle with one leg 2m longer than the other. The hypotenuse is 2m less than twice the length of the shorter leg. Finf the length of the shorter leg. I have tried to solve this but i can't.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We basically have this triangle set up:






Remember, the Pythagorean Theorem is a%5E2%2Bb%5E2=c%5E2 where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.


Since the legs are x and x%2B2 this means that a=x and b=x%2B2


Also, since the hypotenuse is 2x-2, this means that c=2x-2.



a%5E2%2Bb%5E2=c%5E2 Start with the Pythagorean theorem.


x%5E2%2B%28x%2B2%29%5E2=%282x-2%29%5E2 Plug in a=x, b=x%2B2, and c=2x-2


x%5E2%2Bx%5E2%2B4x%2B4=4x%5E2-8x%2B4 FOIL


x%5E2%2Bx%5E2%2B4x%2B4-4x%5E2%2B8x-4=0 Get every term to the left side.


-2x%5E2%2B12x%2B0=0 Combine like terms.


Notice that the quadratic -2x%5E2%2B12x%2B0 is in the form of Ax%5E2%2BBx%2BC where A=-2, B=12, and C=0


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%28-2%29%280%29+%29%29%2F%282%28-2%29%29 Plug in A=-2, B=12, and C=0


x+=+%28-12+%2B-+sqrt%28+144-4%28-2%29%280%29+%29%29%2F%282%28-2%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144-0+%29%29%2F%282%28-2%29%29 Multiply 4%28-2%29%280%29 to get 0


x+=+%28-12+%2B-+sqrt%28+144+%29%29%2F%282%28-2%29%29 Subtract 0 from 144 to get 144


x+=+%28-12+%2B-+sqrt%28+144+%29%29%2F%28-4%29 Multiply 2 and -2 to get -4.


x+=+%28-12+%2B-+12%29%2F%28-4%29 Take the square root of 144 to get 12.


x+=+%28-12+%2B+12%29%2F%28-4%29 or x+=+%28-12+-+12%29%2F%28-4%29 Break up the expression.


x+=+%280%29%2F%28-4%29 or x+=++%28-24%29%2F%28-4%29 Combine like terms.


x+=+0 or x+=+6 Simplify.


So the possible solutions are x+=+0 or x+=+6

Since a length of 0 doesn't make much sense, the only solution is x+=+6


So the legs of the triangle are 6 m and 8 m (add 2) while the hypotenuse is 10 m (double 6 and subtract 2)