Math Problems, Proportions Problems

Problem of the Day: 2/12/13

A 6-foot-tall man stands near a tall tree. His shadow is 8 feet long, and the tree’s shadow is 48 feet long. How tall is the tree?

Solution to yesterday’s problem:

First let’s substitute in the expression in parentheses. 13 ☆ 12 = \sqrt{13^2-12^2}, which you may recognize as two components of a Pythagorean triple. The expression simplifies to 5. Then, 5 ☆ 4 = \sqrt{5^2-4^2}, which you may recognize as two components of a different Pythagorean triple. What a coincidence! The final expression simplifies to give an answer of 3.

Note: I apologize for changing these math problems when I give the solution, but you can imagine how creating a unique, creative, and solvable math problem in the ten minutes before school can lead to interesting mishaps! Anyway, I hope these problems are useful for you.

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