The bases of an isosceles trapezoid are 10 and 24, and the lateral side is 25. Find the height of the trapezoid.

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Drop perpendiculars from the vertices of the smaller base to the larger base.

## Solution

Drop perpendiculars $B M$ and $C N$ from the vertices $B$ and $C$ of the smaller base $B C$ of trapezoid $A B C D$ to the larger base $A D$. Then $A M = D N = \frac{1}{2}(A D - B C) = 7$.

By the Pythagorean theorem, $B M^{2} = 25^{2} - 7^{2} = 18 \cdot 32 = 24^{2}$.

![](https://cdn.mathpix.com/cropped/2024_05_06_c271881b12104a3b803eg-03.jpg?height=320&width=506&top_left_y=277&top_left_x=776)

## Answer

24.