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Having been given the perimeter and perpendicular of a right angled triangle, it is required to find the triangle.
Relationships between Architecture and Mathematics
This 1989 revision of the 1969 NCTM yearbook still provides wonderful suggestions for using the history of mathematics in the classroom.
The incircle O(r) of triangle ABC touches AB at D, BC at E and AC at F. Find r in terms of AD, BE and CF.

An oblong garden is a half yard longer than it is wide and consists entirely of a gravel walk...
These are the winning entries from the annual History of Mathematics SIGMAA Student Paper Contest.
Suppose a ladder 60 feet long is placed in a street so as to reach a window 37 feet above the ground on one side of the street...
Show that the curves x2 - y2 = a2 and 2 xy = b2 cross at right angles.
Whimsical posters of fifteen mathematicians with brief biographies.
A man plants 4 kernels of corn, which at harvest produce 32 kernels: these he plants the second year; now supposing the annual increase to continue 8 fold, what would be the produce of the 15th year, allowing 1000 kernels to a pint?