# Precalculus!

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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! -

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! -

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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