Discussion

The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?

Answer: B

All four sides of a rhombus are equal, so start from the perimeter.

\[ \text{side} = \frac{68}{4} = 17 \text{ cm} \]

\[ \text{half of the given diagonal} = 8 \text{ cm} \]

\[ \text{half of the other} = \sqrt{17^{2} - 8^{2}} = \sqrt{289 - 64} = \sqrt{225} = 15 \text{ cm} \]

\[ \text{other diagonal} = 30 \text{ cm} \]

\[ A = \frac{1}{2} \times 16 \times 30 = 240 \text{ cm}^{2} \]

8–15–17 is another Pythagorean triple, so the second diagonal comes out whole.

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