Question

In the given figure, if $PM=10cm,$ $A\left(△PQS\right)=100sqcm,$ and $A\left(△QRS\right)=110sqcm$, then find the measure of $NR$.
[2 Marks]

Answer 1

$\Delta PQS$ and $\Delta QRS$ have same base QS.

$\frac{A\left(\Delta PQS\right)}{A\left(\Delta QRS\right)}$$=\frac{PM}{NR}$
(1 Mark)

$\therefore \frac{100}{110}=\frac{10}{NR}$

$\therefore NR=\frac{110\times 10}{100}$

$\therefore NR=11cm$
(1 Mark)