SOLUTION: 4. the hypotenuse of a right triangle is 5m long.One leg is 1m longer than the other. Find the lengths of the legs.(SET UP AND SOLVE) I thought I submitted this bt it said did n

Question 187813: 4. the hypotenuse of a right triangle is 5m long.One leg is 1m longer than the other. Find the lengths of the legs.(SET UP AND SOLVE)
I thought I submitted this bt it said did not enter a textbook or something....Anyway, I am very confused by this problem
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 , ,

Square to get .

FOIL

Subtract 25 from both sides.

Combine like terms.

Notice we have a quadratic equation 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

Rewrite as

Add to 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 answers are or

However, you CANNOT have a negative length.

So the only answer is

This means that the first leg "x" is 3 units long

and the second leg "x+1" is 3+1=4 units long

================================================================

Answer:

The legs are 3 and 4 units long.
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