Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

A line is drawn from the origin O to a point P(x,y) in the first quadrant on the graph of y=1/x. From point P, a line is drawn perpendicular to the x-axis, meeting the x-axis at B. Express the perimeter of OPB as a function of x.

I need help setting up the equation for this. Do I just need to determine the equations for each side of the triangle (a, b, c) using the points given. So it would end up looking like x + y + hypotenuse. Then wherever I see a y, I replace it with (1/x) giving me x + (1/x) + x^2 + (1/x)^2.

share|improve this question

1 Answer 1

up vote 4 down vote accepted

You are essentially right. The two "legs" have length $x$ and $1/x$. The hypotenuse is $\sqrt{x^2+1/x^2}$. You just left out the square root symbol. So the perimeter is $$x+\frac{1}{x}+\sqrt{x^2+\frac{1}{x^2}}.$$

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.