SOLUTION: The long side of a right triangle is 5.0 m long. if the hypotenuse is three times the length of the short side, find the short side and the hypotenuse of a right triangle. set up a

Question 948721: The long side of a right triangle is 5.0 m long. if the hypotenuse is three times the length of the short side, find the short side and the hypotenuse of a right triangle. set up and solve a quadratic equation using the Pythagorean formula.
so this what i tried to solve
Pythagorean formula: a^2+b^=c^
I do not know the short side so i used x and 3x for hyp.
Then solve as
(x)^2+(5.0)^2=(3x)^2
x^2+25=9x^2
Now i do not know how to finish solving the equation.
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x, short side
y, long side
h, hypotenuse
-
; .

, Pythagorean Theorem.

-
Substitute the value for y from given.

or

Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!

The long side of a right triangle is 5.0 m long. if the hypotenuse is three times the length of the short side, find the short side and the hypotenuse of a right triangle. set up and solve a quadratic equation using the Pythagorean formula.
so this what i tried to solve
Pythagorean formula: a^2+b^=c^
I do not know the short side so i used x and 3x for hyp.
Then solve as
(x)^2+(5.0)^2=(3x)^2
x^2+25=9x^2
Now i do not know how to finish solving the equation.

I guess by the long side, you mean the longer leg.
You're correct up to that point. Good job!! Continue as follows:

S, or length of shorter side =
Length of hypotenuse: , or
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