Ratio parts sum to 3 + 5 + 7 = 15, giving sides 60 m, 100 m, and 140 m with semi-perimeter s = 150 m. Area = √(150 x 90 x 50 x 10) = 1500√3 m² (approx 2598.08 m²).
The sides of a triangular plot are in the ratio 3: 5: 7; its perimeter is 300 m. Find its area.
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Let the sides be 3x, 5x and 7x meters.
Perimeter = 3x + 5x + 7x = 300 m.
15x = 300, which gives x = 20 m.
The side lengths are:
a = 3 x 20 = 60 m
b = 5 x 20 = 100 m
c = 7 x 20 = 140 m.
Semi-perimeter s = 300 / 2 = 150 m.
Using Heron’s formula:
Area = √(150 x (150 – 60) x (150 – 100) x (150 – 140))
Area = √(150 x 90 x 50 x 10)
Area = √(67,500,000) = 1500√3 m² (approx 2598.08 m²).
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/