A fence 5 feet tall runs parallel to a tall building at a distance of 4 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?

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- November 18th 2009, 08:36 PMsm010291Calculus - Fence over a wall.
A fence 5 feet tall runs parallel to a tall building at a distance of 4 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?

- November 18th 2009, 08:38 PMRockHard
Hint: Try drawing out it really helps, this is basically finding the missing side of a triangle, I believe

- November 18th 2009, 09:04 PMKatherineJK
Use similar triangles.

The smaller triangle has a base of x and a height of 5

The larger triangle has a base of 4+x and and unknown height, y.

Using the ratio, x/5 = (4+x)/y, solve for y and replace that into the formula

x^2 +y^2 = z^2

Take the derivative of z(x) = square root (x squared + y squared)

and find the critical points. Test for a min value and plug x back into

xsquared plus ysquared = zsquared to solve for z (lenght of ladder)

Sorry. That is super confusing without a diagram, but hopefully it somewhat helped.