The length of longest side is 11 units
Solution:
Given that,
The lengths of the sides of a triangle are three consecutive integers
Let the sides be "n" and n + 1 and n + 2
Shortest side = n
longest side = n + 2
Perimeter of triangle = sum of all sides
Perimeter of triangle = n + n + 1 + n + 2
Perimeter of triangle = 3n + 3
Given that,
The length of the shortest side is 30% of the perimeter
Shortest side = n
Therefore,
n = 30 % of perimeter
Which means,
30 % of 3n + 3 = n
[tex]\frac{30}{100} \times (3n + 3) = n\\\\0.3(3n + 3) = n\\\\0.9n + 0.9 = n\\\\n - 0.9n = 0.9\\\\0.1n = 0.9\\\\Divide\ both\ sides\ by\ 0.1\\\\n = 9[/tex]
Therefore,
longest side = n + 2 = 9 + 2 = 11
Thus the length of longest side is 11 units
