Question

Question 5
Write True or False and justify your answer:

If the side of a rhombus is 10cm and one diagonal is 16 cm, then area of the rhombus is 96 $c{m}^2$.

Answer 1

True
Given, side of a rhombus PQRS is 10cm and one of the diagonal is 16cm.
i.e., PQ = QR = RS = SP = 10cm and PR = 16cm

$In\Delta POQ,P{Q}^2=O{P}^2+O{Q}^2$ [by Pythagoras theorem]
[since, the diagonal of rhombus bisects each other at ${90}^{\circ }$]
$\Rightarrow O{Q}^2=P{Q}^2-O{P}^2=(10{)}^2-(8{)}^2$
$\Rightarrow O{Q}^2=100-64=36$
$\Rightarrow OQ=6m$
[taking positive square root because length is always positive]
$\therefore SQ=2\times OQ=2\times 6=12cm$
$\therefore$ Area of the rhombus $=\frac{1}{2}$ (Product of diagonals)
$=\frac{1}{2}(SQ\times PR)=\frac{1}{2}\times 12\times 16=96c{m}^2$