Question

The lengths of the sides of Δ ABC are consecutive integers. It Δ ABC has the same perimeter as an equilateral triangle with a side of length 9 cm, what is the length of the shortest side of ΔABC?

Options

• 4

• 6

• 8

• 10

Answer 1

We are given that triangle ABC has equal perimeter as to the perimeter of an equilateral triangle having side 9 cm. The sides of triangle ABC are consecutive integers. We are asked to find the smallest side of the triangle ABC 

Perimeter of an equilateral triangle, say P having side 9 cm is given by

p = 3a 

a = 9 cm 

p = 3 × 9 

p = 27 cm 

Let us assume the three sides of triangle ABC be x, x+1, x−1

Perimeter of triangle ABC, say P₁ is given by

P₁ = AB + BC + AC

AB = x; BC = x +1; AC = x−1. Since P₁ = P. So

`p_1 = p`

`27 = x + ( x+1) + (x-1) `

`27 = 3x`

`x = 27/3 `

x  =  9 cm 

By using the value of x, we get the sides of triangle as 8 cm, 9 cm and 10 cm