A geometry problem by Saikat Sengupta

Geometry Level 3

The base of a triangle is 15 inches. Two lines are drawn parallel to the base, terminating in the other two sides, and dividing the triangle into three equal areas.

The length of the parallel closer to the base is $\text{\_\_\_\_\_\_\_\_} .$

None of these options

10

7.5

5\sqrt6

1 solution

Mr X
Jun 26, 2018

Relevant wiki: Similar Figures

Let the triangle be $\triangle ABC$ where $BC$ is the base. Then let the parallels be $MN$ and $PQ$ , where $PQ$ is closer to our base $BC$ .

It's obvious that $\triangle APQ \sim \triangle ABC$ , where $|\triangle APQ|:|\triangle ABC|=2:3$ , so $\frac{PQ}{BC}=\sqrt{\frac{2}{3}}$ . Since we know $BC=15$ , $PQ=\frac{15\sqrt{2}}{\sqrt{3}}=5\sqrt{6}$ .

A geometry problem by Saikat Sengupta

1 solution

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