The sides of a triangle are in the ratio 2 : 3 : 4, and its perimeter is 45 cm. Find its area. Class 9

The sides of a triangle are in the ratio 2 : 3 : 4, and its perimeter is 45 cm. Find its area. Class 9

Question 1.

The sides of a triangle are in the ratio 2 : 3 : 4, and its perimeter is 45 cm. Find its area. Class 9

Solution:

Given:

Ratio of sides = 2 : 3 :4

Perimeter of triangle = 45 cm

Let the length of sides be 2x, 3x, 4x cm.

∴ 2x + 3x + 4x = 45

∴ 9x = 45

∴ x = 5

∴ Sides of triangle are 10, 15, 20 cm.

∵ Semi perimeter (s) = $\frac{10+15+20}{2}=\frac{45}{2}$

Using Heron's Formula:

Area of triangle

$\begin{aligned} & \text { Area of triangle }=\sqrt{s(s-a)(s-b)(s-c)} \\ & =\sqrt{\frac{45}{2} \times\left(\frac{45}{2}-10\right)\left(\frac{45}{2}-15\right)\left(\frac{45}{2}-20\right)} \\ & =\sqrt{\frac{45}{2} \times \frac{25}{2} \times \frac{15}{2} \times \frac{5}{2}} \\ & =\frac{75 \sqrt{15}}{4}\end{aligned}$

∴ Area of triangle = $\frac{75 \sqrt{15}}{4}$ cm²