$\left.\begin{array}{l}\text { Rhombuses. Properties and characteristics }\end{array}\right]$

The diagonals of a rhombus are 24 and 70. Find the side of the rhombus.
Use the properties of the diagonals of a rhombus.

## Solution

The diagonals of a rhombus are perpendicular to each other and bisect each other at their point of intersection. The side of the rhombus is the hypotenuse of a right triangle, with the legs being half the lengths of the diagonals. By the Pythagorean theorem, \(a^{2} = 12^{2} + 35^{2} = 37^{2}\)

![](https://cdn.mathpix.com/cropped/2024_05_06_34fd2032e75750f56a92g-03.jpg?height=346&width=560&top_left_y=1596&top_left_x=749)

## Answer

37.