Question

If the base of an isosceles triangle is 6 cm and its perimeter is 16 cm, then its area is 12 cm².

Answer 1

True
Let the equal sides of the isosceles triangle be a cm each.
We have:
Base of the triangle, b = 6 cm
Perimeter = 16 cm
or, a + a + 6 = 16
or, 2a = 10
or, a = 5 cm

Now,
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{isosceles}\mathrm{triangle}=\frac{b}{4}\sqrt{4a^2-b^2} \\ \mathrm{Here}, \\ a=5\mathrm{cm}\mathrm{and}b=6\mathrm{cm} \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \frac{6}{4}\times \sqrt{4(5{)}^2-6^2} \\ =1.5\times \sqrt{100-36} \\ =1.5\times \sqrt{64} \\ =1.5\times 8 \\ =12{\mathrm{cm}}^2 \end{gathered}$$