Explanation:
The longest side of the triangle is equal to the sum of the other two sides. Therefore, the longest side = (x + y), where x and y are the lengths of the other two sides.
We also know that twice the shortest side is 6 cm less than the longest side, which means 2x = (x + y) - 6.
So we can solve for x and y:
x + y = 74
2x = (x + y) - 6
Substituting for (x + y) in the second equation, we have:
2x = 74 - 6
2x = 68
x = 34
Substituting x into the first equation, we have:
y = 74 - 34
y = 40
Therefore, the lengths of the sides of the triangle are 34 cm, 40 cm, and 74 cm.