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?

(a) 4

(b) 6

(c) 8

(d) 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

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

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

Therefore, the answer is (c).