Question

An equilateral triangle of sides 3 inch each is given. How many equilateral triangles of side 1 inch can be formed from it ?

Answer 1

Divide each side into 3 equal parts. Each part will be of 1 inch. 

so

small triangle= original triangle

Area of triangle = (√3/4)a^2

Let number of 1 inch triangle = n

∴ n × (√3/4) 1^2 = (√3/4) × 3^2

⇒ n = 9

$hope \: its \: helpful$

Answer 2

The number of small triangles formed are 9.

Given:-

Side of the equilateral triangle = 3inch

Side of smaller equilateral triangle = 1inch

To Find:-

The number of small triangles formed.

Solution:-

We can easily find out the number of small triangles formed by using these simple steps.

As

Side of the equilateral triangle (a1) = 3inch

Side of smaller equilateral triangle (a2) = 1inch

Also, let the number of small triangles be n.

So, here we will conserve the area of both the triangles by

Area of large triangle = n × Area of small triangles

According to the formula of area of equilateral triangle,

$a = \frac{ \sqrt{3} }{4} \times {(side)}^{2}$

So,

$a1 = n \times a2$

i.e.

$\frac{ \sqrt{3} }{4} \times {a1}^{2} =n \times \frac{ \sqrt{3} }{4} \times {a2}^{2}$

on cancelling √3/4 from both sides,

${a1}^{2} = n \times {a2}^{2}$

On putting the values,

${3}^{2} = n \times {1}^{2}$

$9 = n \times 1$

$n = 9$

Hence, The number of small triangles formed are 9.

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