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

Algebra ->  Pythagorean-theorem -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
x, short side
y, long side
h, hypotenuse
-
y=5.0; h=3x.

x%5E2%2By%5E2=h%5E2, Pythagorean Theorem.
x%5E2=%283x%29%5E2-y%5E2
x%5E2=9x%5E2-y%5E2
x%5E2-9x%5E2=-y%5E2
9x%5E2-x%5E2=y%5E2
8x%5E2=y%5E2
x%5E2=%281%2F8%29y%5E2
x=sqrt%28y%5E2%2F8%29
-
Substitute the value for y from given.
x=sqrt%28%285%5E2%29%2F8%29

x=5sqrt%281%2F8%29

x=%285%2F4%29sqrt%281%2F2%29 or %285%2F4%29%2Fsqrt%282%29

%28%285%2F4%29%2Fsqrt%282%29%29%28sqrt%282%29%2Fsqrt%282%29%29

%285%2Asqrt%282%29%29%2F%284%2A2%29

highlight%28x=%285%2F8%29sqrt%282%29%29

Answer by MathTherapy(10552) About Me  (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:

9x%5E2+-+x%5E2+=+25

8x%5E2+=+25

x%5E2+=+25%2F8

x+=+sqrt%2825%2F8%29

x+=+sqrt%2825%29%2F2sqrt%282%29

x+=+5sqrt%282%29%2F%282+%2A+2%29

S, or length of shorter side = 5sqrt%282%29%2F4

Length of hypotenuse: 3%285sqrt%282%29%2F4%29, or highlight_green%2815sqrt%282%29%2F4%29