Question

The unequal side of an isosceles $\Delta$ is $6$ cm and its perimeter is $24$ cm. Finds its area .

• A. $12\sqrt{2}$ sq. cm
• B. $14\sqrt{2}$ sq. cm
• C. $18\sqrt{2}$ sq.cm
• D. $24\sqrt{2}$ sq. cm

Answer 1

Answer: (C)

$18\sqrt{2}$ sq.cm

$\text{Perimeter = Sum of side}$

from given values,

$24=x+x\text{+ 6}$

$24-6=2x$

$18=2x$

$x=9$

$s=\frac{a+b+c}{2}=\frac{6+9+9}{2}=12$

$Area=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$

$\sqrt{12\left(9-6\right)\left(9-6\right)\left(12-6\right)}$

$=\sqrt{12\left(3\right)\left(3\right)\left(6\right)}$

$=\sqrt{6\times 2\times 3\times 3\times 6}$

$=18\sqrt{2}c{m}^2$