Posted by **Solta** on Saturday, October 13, 2012 at 11:27pm.

A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (3,2). write the length L of hypotenuse as a function of x.

- Math -
**Reiny**, Sunday, October 14, 2012 at 12:52am
Let the x-intercept of the line be (x,0)

let the y-intercept of the line be (0,y)

we have similar triangles, and by ratios ...

y/x = 3/(x-2)

xy - 2y = 3x

y(x-2) = 3x

y = 3x/(x-2)

L^2 = x^2 + y^2

= x^2 + [3x/(x-2)]^2

= x^2 + 9x^2/(x^2 - 4x + 4)

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