The lengths of the sides of a triangle are three consecutive integers. The length of the shortest side is 30% of the perimeter. What is the length of the longest side?

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

Therefore,

longest side = n + 2 = 9 + 2 = 11

Thus the length of longest side is 11 units

7

step-by-step explanation:

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x