The area of a rhombus is 96 square cm and one of its diagonals is of length 12 cm. What is the perimeter of the rhombus?

Explanation

Area = \frac{1}{2} d_1 d_2 \implies 96 = \frac{1}{2}(12)d_2 \implies d_2 = 16\text{ cm}. The side of the rhombus is a = \sqrt{(\frac{12}{2})^2 + (\frac{16}{2})^2} = \sqrt{36+64} = 10\text{ cm}. The perimeter is 4a = 40\text{ cm}.

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