Posted by **kajal** on Friday, September 16, 2011 at 6:18pm.

So I have this major assignment due, and I cant seem to figure this one out:

A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (5, 3). Write the length L of the hypotenuse as a function of x(the x-intercept of the line).

Can someone please help me on this problem? The answer has to be in the most simplified version possible. An explanation would greatly be appreciated. thank you

- Precalculus! -
**Reiny**, Friday, September 16, 2011 at 11:34pm
Make a sketch

let the x-intercept be (x,0) and the y-intercept (0,y)

Draw an altitude from (5,3) to the x-axis

I see two similar right-angled triangles

By ratios:

y/x = 3/(x-5)

y = 3x/(x-5)

L^2 = x^2 + y^2

= x^2 + 9x^2/(x-5)^2

L = √( x^2 + 9x^2/(x-5)^2 )

= √[ (x^2(x-5)^2 + 9x^2)/(x-5)2 ]

= 1/(x-5) √[ x^2(x-5)^2 + 9 ]

= x/(x-5) √ (x^2 - 10x + 34 )

- Precalculus! -
**kajal**, Monday, September 19, 2011 at 10:36pm
thanks...i got that..the problem is i cant put that into webassign..it wont take my answer....how can i further simplify this answer

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