SOLUTION: One leg of a right triangle is 1 in. shorter than the other leg. The hypotenuse is 4 in. longer than the shorter side. Find the length of each side.

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Question 360165: One leg of a right triangle is 1 in. shorter than the other leg. The hypotenuse is 4 in. longer than the shorter side. Find the length of each side.
Found 2 solutions by solver91311, ewatrrr:
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Let represent the measure of the shortest leg. Then represents the measure of the other leg and represents the measure of the hypotenuse.

With a tip o' the hat to Mr. Pythagoras we write:

Expand the binomials:

Collect like terms in the LHS:

Solve the quadratic for . Then compute and .

Hint #1: This does not factor. Use the Quadratic Formula (or complete the square if you are glutton for punishment).

Hint #2: Since the problem doesn't give you a round-off precision, it must want the exact answer. Hence, leave your answer in radical form. However, you will need to estimate the numerical approximation to determine whether either of your answers are negative. Since you are looking for a positive measure of length, you need to discard any negative root.

John

My calculator said it, I believe it, that settles it

Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website!

Hi,
Let x represent the shorter side. then (x+1) is the other leg and the hypothenuse is (x+4)
Applying the Pythagorean Theorem
x^2 +(x+1)^2 = (x+4)^2
solving for x
x^2 + x^2 +2x + 1 = x^2 + 8x + 16
x^2 -6x + -15
Using Quadratic Equation to Solve