The perimeter of a rhombus is 100 meters and one of its diagonals is 14 meters long. What is the length of the other diagonal?
48 meters
All four sides of a rhombus are equal, so each side is \(\frac{100}{4} = 25\) meters.
The diagonals of a rhombus bisect each other at right angles, so each side, together with the two half-diagonals, forms a right-angled triangle: \(\left(\frac{d_1}{2}\right)^2 + \left(\frac{d_2}{2}\right)^2 = \text{side}^2\).
One diagonal is 14 meters, so its half is \(\frac{14}{2} = 7\) meters.
Substitute: \(7^2 + \left(\frac{d_2}{2}\right)^2 = 25^2\), which gives \(49 + \left(\frac{d_2}{2}\right)^2 = 625\).
So \(\left(\frac{d_2}{2}\right)^2 = 576\) and \(\frac{d_2}{2} = 24\), giving \(d_2 = 48\) meters.
Hence, the length of the other diagonal is 48 meters.
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