Math CentralQuandaries & Queries


Question from Dylan:

The area of a triangle is 108in squared. A base and corresponding height are in the ratio 3:2. Find the length of the base and the corresponding height

Hi Dylan,

Let $x$ inches be one third the length of the base then the base is $3x$ inches long. Since the ratio of the base to the height is 3:2 the height is $2x$ inches. Use the fact that the area of the triangle is $\large \frac12 \normalsize \mbox{ the base } \times \mbox{ the height}$ to write an expression for the area of the triangle. But the area is 108 square inches. Solve for $x.$


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