algebra
posted by ac .
a 13 foot ladder is placed so that it reaches to a point on the wall that is 2 feet higher than twice the distance from the base of the wall to the base of the ladder. How high does the ladder reach?

x is the distance from base to wall
x^2 + (2x+2)^2 = 13^2
Now, you can expand that and solve for x, but the obvious hint is the 13' ladder. One of the common integersided triangles is the 51213, where the lengths just exactly fit our problem.
The base is 5' from the wall, and the ladder top is 12' off the ground.