NCERT Class 9 Solutions: Heron's Formula (Chapter 12) Exercise 12.1 Part 2

Herons Formula and its components

Herons Formula

Herons Formula and its components

Q-5 Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm . Find its area.Solution:

  • Ratio of the sides of the triangle =12:17:25

  • Let the common ratio be x then sides are 12x,17xand25x

    Perimeter of the triangle =540cm

    • 12x+17x+25x=540cm ( p=a+b+c )

    • 54x=540cm

    • x=10

    Sides of triangle are,

  • 12x=12×10=120cm ( x=10 )

  • 17x=17×10=170cm ( x=10 )

  • 25x=25×10=250cm ( x=10 )

Semi perimeter of triangle(s)

  • 5402=270cm

Using heron's formula, area of the triangle

  • =s(sa)(sb)(sc)

  • =270(270120)(270170)(270250)cm2

  • =270×150×100×20cm2

  • =9000cm2

Q-6 An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.Solution:

  • Length of the equal sides =12cm

  • Perimeter of the triangle =30cm

  • Length of the third side =30(12+12)cm=6cm (perimeter=a+b+c)

  • Semi perimeter of the triangle(s) =302cm=15cm

  • Using heron's formula, area of the triangle

    • =s(sa)(sb)(sc)

    • =15(1512)(1512)(156)cm2

    • =15×3×3×9cm2

    • =915cm2

Explore Solutions for Mathematics

Sign In