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 yaxes and a line through the point (5, 3). Write the length L of the hypotenuse as a function of x(the xintercept 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 xintercept be (x,0) and the yintercept (0,y)
Draw an altitude from (5,3) to the xaxis
I see two similar rightangled triangles
By ratios:
y/x = 3/(x5)
y = 3x/(x5)
L^2 = x^2 + y^2
= x^2 + 9x^2/(x5)^2
L = √( x^2 + 9x^2/(x5)^2 )
= √[ (x^2(x5)^2 + 9x^2)/(x5)2 ]
= 1/(x5) √[ x^2(x5)^2 + 9 ]
= x/(x5) √ (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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