Question

Tick (✓) the correct answer
The lengths of the diagonals of a rhombus are 16 cm and 12 cm. The length of each side of the rhombus is
(a) 8 cm
(b) 9 cm
(c) 10 cm
(d) 12 cm

Answer 1

$\left(\mathrm{c}\right)10\mathrm{cm}$


$$\begin{gathered} \mathrm{Let}ABCD\mathrm{be}\mathrm{a}\mathrm{rhombus}. \\ L\mathrm{et}AC\mathrm{and}BD\mathrm{be}\mathrm{the}\mathrm{diagonals}\mathrm{of}\mathrm{the}\mathrm{rhombus}\mathrm{intersecting}\mathrm{at}\mathrm{a}\mathrm{point}O. \\ AC=16\mathrm{cm} \\ BD=12\mathrm{cm} \\ \mathrm{We}\mathrm{know}\mathrm{that}\mathrm{the}\mathrm{diagonals}\mathrm{of}\mathrm{a}\mathrm{rhombus}\mathrm{bisect}\mathrm{each}\mathrm{other}\mathrm{at}\mathrm{right}\mathrm{angles}. \\ \therefore AO=\frac{1}{2}AC \\ =\left(\frac{1}{2}\times 16\right)\mathrm{cm} \\ =8\mathrm{cm} \\ BO=\frac{1}{2}BD \\ =\left(\frac{1}{2}\times 12\right)\mathrm{cm} \\ =6\mathrm{cm} \\ \mathrm{From}\mathrm{the}\mathrm{right}∆AOB: \\ A{B}^2=A{O}^2+B{O}^2 \\ =\left\{{\left(8\right)}^2+{\left(6\right)}^2\right\}{\mathrm{cm}}^2 \\ =\left(64+36\right){\mathrm{cm}}^2 \\ =100{\mathrm{cm}}^2 \\ \Rightarrow AB=\sqrt{100}\mathrm{cm} \\ =10\mathrm{cm} \\ \mathrm{Hence},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{side}ABis10\mathrm{cm}. \\ \mathrm{Therefore},\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{side}\mathrm{of}\mathrm{the}\mathrm{rhombus}\mathrm{is}10\mathrm{cm}\mathrm{because}\mathrm{all}the\mathrm{sides}\mathrm{of}a\mathrm{rhombus}\mathrm{are}\mathrm{equal}. \end{gathered}$$