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.

⇒ AC² = AD² + CD²

⇒ 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