Posted by **Anonymous** on Friday, October 28, 2011 at 1:19pm.

A fence 2 feet tall runs parallel to a tall building at a distance of 6 feet from the building. What is the length of the shortest ladder that will reach from the ground over the fence to the wall of the building?

- Calculus -
**Steve**, Friday, October 28, 2011 at 4:49pm
Let the ladder length be d

Let the base of the ladder be x feet from the fence, and hit the wall at height h.

from similar triangles,

2/x = h/(6+x)

h = 2(x+6)/x

d^2 = (6+x)^2 + h^2

= (x+6)^2 + 4(x+6)^2/x^2

= (x+6)^2 * (1 + 4/x^2)

d^2 (and therefore d) has a minimum at x = 2.9

d^2 = 116.88

d = 10.8 ft

## Answer this Question

## Related Questions

- Calculus - A fence 5 feet tall runs parallel to a tall building at a distance of...
- Math: Calculus - A fence 6 feet tall runs parallel to a tall building at a ...
- Calculus - A fence 4 feet tall runs parallel to a tall building at a distance of...
- Calculus - fence 3 feet tall runs parallel to a tall building at a distance of ...
- Calculus - A fence 3 feet tall runs parallel to a tall building at a distance of...
- Calculus - A fence 8 feet tall runs parallel to a tall building at a distance of...
- calculus - A fence 5 feet tall runs parallel to a tall building at a distance ...
- calculus - A fence 5 feet tall runs parallel to a tall building at a distance ...
- Calculus - A fence 4 feet tall runs parallel to a tall building at a distance of...
- Calculus - A fence 6 feet tall runs parallel to a tall building at a distance of...

More Related Questions