Question

Draw an equilateral triangle of height 2.6 cm. Draw another triangle similar to itsuch that its side is 2/3 of the side of the first

Answer 1

Answer:

The measure of each side of another equilateral triangle is 2.785 cm .

Step-by-step explanation:

Given as :

For an equilateral triangle

The height of triangle = h = 3.6 cm

Let The each side of equilateral triangle = a cm

Let The each side of another equilateral triangle = a' cm

According to question

∵ Height of equilateral triangle = × side

i.e h = × a

or, 3.6 cm = × a

or, 3.6 cm = 0.866 × a

Or, a =

∴   a = 4.157 cm

So, The each side of equilateral triangle = a = 4.157 cm

Again

Another Triangle similar to first equilateral triangle ,

The each side of another equilateral triangle = × side of first triangle

i.e a' = × a

or, a' = × 4.157 cm

Or, a' = 0.67 × 4.157 cm

∴ a' = 2.785 cm

So, The each side of another equilateral triangle = a' = 2.785 cm

Hence, The measure of each side of another equilateral triangle is 2.785 cm .

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