Question

Find the area of a triangle whose two sides are $8$ cm and $11$cm and the perimeter is $32$cm.

• A. $8c{m}^2$
• B. $8\sqrt{30}c{m}^2$
• C. $\frac{8}{\sqrt{30}}c{m}^2$
• D. $24c{m}^2$

Answer 1

The correct option is B $8\sqrt{30}c{m}^2$

Let third side be $x$

Perimeter $=8+11+x$

$19+x=32$

$x=13$

$s=\frac{32}{2}=16$

Heron's formula

$A=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{16(16-8)(16-11)(16-13)}$

$=\sqrt{16\times 8\times 5\times 3}$

$=8\sqrt{30}c{m}^2$