Question

# The diagonals of a rhombus are 16 cm and 12 cm. Find the length of each side of the rhombus.

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Solution

## All the sides of a rhombus are equal in length. The diagonals of a rhombus intersect at ${90}^{\circ }$. The diagonal and the side of a rhombus form right triangles. In $△AOB$: $A{B}^{2}=AO{}^{2}+O{B}^{2}\phantom{\rule{0ex}{0ex}}={8}^{2}+{6}^{2}\phantom{\rule{0ex}{0ex}}=64+36\phantom{\rule{0ex}{0ex}}=100\phantom{\rule{0ex}{0ex}}AB=10\mathrm{cm}$ Therefore, the length of each side of the rhombus is 10 cm.

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