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
Area of the triangle = 9000 cm2.
☛ Check: NCERT Solutions for Class 9 Maths Chapter 12
Video Solution:
Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.
Class 9 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 5
Summary:
It is given that sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. We have found that its area is 9000 cm2.
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