Sides are 2x, 3x, 4x with sum 9x = 45, giving sides 10 cm, 15 cm, 20 cm. Semi-perimeter s = 22.5 cm. By Heron’s formula, area = √(22.5 x 12.5 x 7.5 x 2.5) = (75/4)√15 cm² (approx 72.62 cm²).
The sides of a triangle are in the ratio 2: 3: 4 and its perimeter is 45 cm. Find its area.
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Let the side lengths be 2x, 3x and 4x.
Perimeter = 2x + 3x + 4x = 9x = 45 cm, so x = 5 cm.
The sides are a = 10 cm, b = 15 cm, c = 20 cm.
Semi-perimeter s = 45 / 2 = 22.5 cm.
Using Heron’s formula:
Area = √(s(s – a)(s – b)(s – c))
Area = √(22.5 x (22.5 – 10) x (22.5 – 15) x (22.5 – 20))
Area = √(22.5 x 12.5 x 7.5 x 2.5)
Area = √[(45/2) x (25/2) x (15/2) x (5/2)]
Area = √(84375 / 16) = (75 / 4)√15 cm² (approximately 72.62 cm²).
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/