Question 1194769
We are given that the lengths of the sides of a triangle are consecutive even integers.

Let the sides of the triangle be x,x+2 and x+4 respectively.

We are given that the length of the longest side is 14 units shorter than the perimeter.

The length of the longest side=x+4 units

The perimeter of the triangle = x+x+2+x+4=3x+6 units

Plugging in the values we get,

x+4=3x+6-14
x+4=3x-8
x+4+8=3x
x+12=3x
3x-x=12
2x=12
x=6 units

The longest side of the triangle is 6+4=10 units

The lengths of the triangle are 6,8 and 10 units respectively.

The perimeter of the triangle is 6+8+10=24 units

10=24-14

The longest side is 14 units shorter than the perimeter of the triangle.

Thus, the solution is correct.Hence,proved.

Hence,the longest side of the triangle is 10 units.