Question

The sides of a triangle are in the ratio 2 : 3 : 4. The perimeter of the triangle is 18 cm. The area (in sq.cm) of the triangle is

• A. 9
• B. 36
• C. $$\sqrt{42}$$
• D. $$3\sqrt{15}$$

Answer 1

Answer:

$$3\sqrt{15}$$

Ratio = 2 : 3 : 4 = 4 : 6 : 8

Perimeter = 18 cm

Semi-perimeters $=\frac{4+6+8}{2}=9$

Area of triangle $=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{9(9-4)(9-6)(9-8)}$

$=\sqrt{9\times{5}\times{3}\times{1}}$

$=3\sqrt{15}$sq.cm