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. 
<pre>I guess by the long side, you mean the longer leg. 

You're correct up to that point. Good job!! Continue as follows:
{{{9x^2 - x^2 = 25}}}
{{{8x^2 = 25}}}
{{{x^2 = 25/8}}}
{{{x = sqrt(25/8)}}}
{{{x = sqrt(25)/2sqrt(2)}}}
{{{x = 5sqrt(2)/(2 * 2)}}}
S, or length of shorter side = {{{5sqrt(2)/4}}}
Length of hypotenuse: {{{3(5sqrt(2)/4)}}}, or {{{highlight_green(15sqrt(2)/4)}}}