# The picture shows an equilateral triangle cut into halves by a line through vertex. i) What is the perimeter of a part?ii) How much less than the perimeter of the whole triangle is this? Consider ΔACD,

We know that in a right angled triangle, the square of tshe hypotenuse is equal to the sum of the squares of the other two sides.

22 = 12 + CD2

4 = 1 + CD2

CD2 = 4 – 1 = 3

AC = √3 m

√3 ≈ 1.73 m

We know that perimeter of a polygon is the sum of all its sides.

(i) Here, ΔACD is a part.

Perimeter = 2 + 1 + √3

= 3 + √3

3 + √3 = 3 + 1.73 = 4.73 m

Perimeter of a part of the given equilateral triangle = 4.73 metres

(ii) Perimeter of the whole triangle = 2 + 2 + 2 = 6 metres

The perimeter of a part is less than the whole by,

6 – 4.73 = 1.27 metres

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