Question

The perimeter of a triangle is 540 m and its sides are in the
ratio 12 : 25 : 17.
(i) Find the area of the triangle.
(ii) Also find the length of its altitude corresponding to the
largest side.

Answer 1

Step-by-step explanation:



Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.

Solution:

Given: Ratio of sides of the triangle and its perimeter.

By using Heron’s formula, we can calculate the area of a triangle.

Heron's formula for the area of a triangle is: Area = √s(s - a)(s - b)(s - c)

Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the perimeter of the triangle

Since the ratios of the sides of the triangle are given as 12:17:25

So, we can assume the length of the sides of the triangle as 12x cm, 17x cm, and 25x cm.



So the perimeter of the triangle will be 

Perimeter = 12x + 17x + 25x 

12x + 17x + 25x = 540 (given)

54x = 540

x = 540/54

x = 10 cm

Therefore, the sides of the triangle:

12x = 12 × 10 = 120 cm, 17x = 17 × 10 = 170 cm, 25x = 25 × 10 = 250 cm

a = 120cm, b = 170 cm, c = 250 cm

Semi-perimeter(s) = 540/2 = 270 cm

By using Heron’s formula,

Area of a triangle = √s(s - a)(s - b)(s - c)

= √270(270 - 120)(270 - 170)(270 - 250)

= √270 × 150 × 100 × 20

= √81000000

= 9000 cm2