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The perimeter of the rhombus is 48, and the sum of the diagonals is 26. Find the area of the rhombus.
Let \( x \) and \( y \) be the halves of the diagonals of the rhombus and form a system of equations with respect to \( x \) and \( y \).

## Solution

Let \( x \) and \( y \) be the halves of the diagonals of the rhombus. Since the side of the rhombus is \( \frac{48}{4}=12 \), then

\[
\left\{\begin{array}{l}
x+y=13 \\
x^{2}+y^{2}=144 .
\end{array}\right.
\]

Square both sides of the first equation and subtract the second equation from the result. We get that \( 2xy = 169 - 144 = 25 \). This is the area of the rhombus.

## Answer

25.