Question

The sides of triangle are $4,5,6$ then area in sq.units is

• A. $\frac{15}{4}\sqrt{7}$
• B. $\frac{3}{2}\sqrt{7}$
• C. $\frac{3}{2}$
• D. $\frac{7}{2}$

Answer 1

The correct option is A $\frac{15}{4}\sqrt{7}$

Given: $a=4,b=5,c=6$
$s=\frac{a+b+c}{2}=\frac{4+5+6}{2}=\frac{15}{2}$
$\Delta =\sqrt{s(s-a)(s-b)(s-c)}$
$\Delta =\sqrt{\frac{15}{2}(\frac{15}{2}-4)(\frac{15}{2}-5)(\frac{15}{2}-6)}$
$\Delta =\sqrt{\frac{15}{2}\cdot \frac{7}{2}\cdot \frac{5}{2}\cdot \frac{3}{2}}$
$\Delta =\frac{15}{4}\sqrt{7}\text{sq.units}$