NCERT Class 9 Solutions: Triangles (Chapter 7) Exercise 7.5 – Part 4

Equilateral triangle

3 equilateral triangels with 3 equal sides and angles (60 degree each)

Equilateral Triangle With 3 Equal Sides and Angles

3 equilateral triangels with 3 equal sides and angles (60 degree each)

In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, equilateral triangles are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.

Q-4 Complete the hexagonal rangoli and the star rangolies (See figure) but filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?

A rangoli (floor design) with hexagon and star described in question

A Rangoli (Floor Design) With Hexagon and Star

A rangoli (floor design) with hexagon and star described in question

Solution:

  • In hexagonal, Number of equilateral triangles each of side 5 cm are 6.

  • Area of equilateral triangle = 34(side)2=34(5)2=34×25sq.cm

  • Area of hexagonal = 6× Area of an equilateral triangle rangoli

    =6×34×25=150×34sq.cm ……………………..equation(1)

  • Now area of equilateral triangle of side 1cm==34(side)2=34(1)2=34sq.cm ………..equation(2)

  • Number of equilateral triangles each of side 1cm in hexagonal rangoli

    =150×34÷34=150×34×43=150 ………………equation(3)

  • Now in star

  • Number of equilateral triangles each of side 5 cm=12

  • Therefore , total area of star =12× area of an equilateral triangle of side 5cm

    =12×(34(5)2)

    =12×(34×25)

    =30034sq.cm ……….equation(4)

  • Number of equilateral triangles each of side 1 cm in star

    =30034÷34

    =30034×43

    =300 ……….equation (4)

  • From eq. (3) and (4), we observe that star has more equilateral triangles each of side 1 cm.

Explore Solutions for Mathematics

Sign In