Question

The sides of a triangle are 7cm, 9cm, 14cm. Its area is

• A. $12\sqrt{5}c{m}^2$
  
• B. $12\sqrt{3}c{m}^2$
  
• C. $24\sqrt{5}c{m}^2$
  
• D. $63c{m}^2$

Answer 1

The correct option is A

$12\sqrt{5}c{m}^2$

Sides of a triangle are 7 cm, 9cm and 14 cm
$\therefore s=\frac{a+b+c}{2}=\frac{7+9+14}{2}=\frac{30}{2}=15$
$\therefore Area=\sqrt{s(s-a)(s-b)(s-c)}$
= $\sqrt{15(15-7)(15-9)(15-14)}$
= $\sqrt{15\times 8\times 6\times 1}=\sqrt{720}=\sqrt{144\times 5}$
= $12\sqrt{5}c{m}^2$