Question

The area of a triangle of sides 7 m, 8 m and 9 m is equal to $m^2$.

• A. $5\sqrt{5}$
• B. $5\sqrt{12}$
• C. $12\sqrt{5}$

Answer 1

The correct option is C $12\sqrt{5}$

Let $a,b\text{and}c$ be the sides of the triangle.
Given :$a=7\text{m};b=8\text{m}\text{and}c=9\text{m}\text{Semi-perimeter of a triangle,}s=\frac{a+b+c}{2}s=\frac{7+8+9}{2}=\frac{24}{2}=12m\text{Using Heron's formula for area of a triangle,}A=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{\left(12\right)(12-7)(12-8)(12-9)}\therefore A=\sqrt{\left(12\right)\left(5\right)\left(4\right)\left(3\right)}=12\sqrt{5}{m}^2$