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
Solution
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
