Math CentralQuandaries & Queries


Question from mike:

How do you find the length of the base or the height of a triangle if the area is 30 square feet?


The short answer is that you can't. Triangles of many different shapes and many different base lengths and heights all have the same area of 30 square feet. Take any two positive numbers which have their product equal to 30, say 5 and 6. Double one of them, 10 = 2 × 5. Any triangle with base length 10 feet and height 6 feet has area

1/2 × base × height = 1/2 × 10 × 6 = 30 square feet.

This works for any two positive numbers which have a product of 30, integers or not.


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