Question

A fence 4 feet tall runs parallel to a tall building at a distance of 3 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?

Answer 1

the shortest hypotenuse would be a 45, 45 degree triangle. The hypotenuse of a 4 by 4 by h triangle is sqrt(16 + 16) = sqrt(32). The hypotenuse of a 3x3 triangle is sqrt(9 + 9) = sqrt(18). add them together.

Answer 2

The reason Andy's answer works is by using the rule of similar triangles. Yes, an isosceles triangle with 45 degree angles would create the shortest hypotenuse in this case. If you draw a diagram, you can create two triangles, one from the fence to the ground using the height of fence (4ft x 4ft) and another from the fence to the building using the distance outward (3ft x 3ft). Once you find the two hypotenuses, just add them together to get the total length. (Find the hypotenuse using sqrt(side1 + side2).)