Question

Mark (✓) against the correct answer in each of the following:
Each side of a rhombus is 10 cm long and one of its diagonals measures 16 cm. The length of the other diagonal is
(a) 6 cm
(b) 12 cm
(c) 13 cm
(d) $\sqrt{156}\mathrm{cm}$

Answer 1

(b) 12 cm




We know that the diagonals of a rhombus bisect each other at right angles.
So, BO = OD = 8 cm
$$\begin{gathered} \mathrm{In}\mathrm{right}-\mathrm{angled}\mathrm{triangle}AOB, \\ A{O}^2+B{O}^2=A{B}^2 \\ \Rightarrow AO=\sqrt{A{B}^2-B{O}^2} \\ =\sqrt{{10}^2-8^2} \\ =\sqrt{100-64} \\ =\sqrt{36} \\ =6\mathrm{cm} \\ \mathrm{So},AC=2AO=2\times 6=12\mathrm{cm} \end{gathered}$$