Discussion

The side of a rhombus is 26 m and length of one of its diagonals is 20 m. The area of the rhombus is?

Answer: D

The diagonals of a rhombus bisect each other at right angles, so half of each and a side form a right triangle.

\[ \text{half of the known diagonal} = 10 \text{ m} \]

\[ \text{half of the other} = \sqrt{26^{2} - 10^{2}} = \sqrt{676 - 100} = \sqrt{576} = 24 \text{ m} \]

\[ \text{other diagonal} = 48 \text{ m} \]

\[ A = \frac{1}{2} \times 20 \times 48 = 480 \text{ m}^{2} \]

10–24–26 is the 5–12–13 triple doubled.

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