Question

In $△PQR,PQ=4cm,PR=8cm$ and $RT=6cm$.

Find (i) the area of $△PQR$ (ii) the length of $QS$.

• A. (i) $12c{m}^2$ (ii) $3cm$.
• B. (i) $10c{m}^2$ (ii) $3cm$.
• C. (i) $12c{m}^2$ (ii) $2cm$.
• D. None of these

Answer 1

The correct option is A (i) $12c{m}^2$ (ii) $3cm$.

Let the base of the triangle be $PQ=4cm$, then the height is $RT=6cm$.

Hence area of triangle

$=\frac{1}{2}base\times height=\frac{1}{2}\left(4\right)\left(6\right)=12c{m}^2$

Now $A=12c{m}^2$

Hence,

$\frac{1}{2}PR\times QS=12$

$⟹\frac{1}{2}\times 8\times QS=12$

$⟹QS=3cm$