Question

The base of an isosceles triangle is 16 cm and its area is 48 cm². The perimeter of the triangle is
(a) 41 cm
(b) 36 cm
(c) 48 cm
(d) 324 cm

Answer 1

(b) 36 cm

Let $△$PQR be an isosceles triangle and PX$\perp$QR.
Now,
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{triangle}=48{\mathrm{cm}}^2 \\ \Rightarrow \frac{1}{2}\times QR\times PX=48 \\ \Rightarrow h=\frac{96}{16}=6\mathrm{cm} \\ \mathrm{Also},\mathit{} \\ QX\mathit{}=\frac{1}{2}\times 24=12\mathrm{cm}\mathrm{and}PX=12\mathrm{cm} \end{gathered}$$
$$\begin{gathered} PQ=\sqrt{Q{X}^2+P{X}^2} \\ a=\sqrt{8^2+6^2}=\sqrt{64+36}=\sqrt{100}=10\mathrm{cm} \end{gathered}$$

∴ Perimeter = (10 + 10 + 16) cm = 36 cm