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

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) (Show Source): You can put this solution on YOUR website!
We basically have this triangle set up:

Remember, the Pythagorean Theorem is where "a" and "b" are the legs of a triangle and "c" is the hypotenuse.

Since the legs are and this means that and

Also, since the hypotenuse is , this means that .

Start with the Pythagorean theorem.

Plug in , , and

FOIL

Get every term to the left side.

Combine like terms.

Notice that the quadratic is in the form of where , , and

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

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Take the square root of to get .

or Break up the expression.

or Combine like terms.

or Simplify.

So the possible solutions are or

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

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)
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