The perimeter of a triangle is 62 cm. If the second side is twice as long as the first side, and the third side is 12 cm longer than the second side, what is the length of the longest side of the triangle?

x

Let's call the length of the first side of the triangle as "x" cm.

According to the given information, the second side is twice as long as the first side, so its length would be 2x cm.

The third side is 12 cm longer than the second side, so its length would be 2x + 12 cm.

The perimeter of a triangle is calculated by adding the lengths of all three sides, so we have:

x + 2x + (2x + 12) = 62 cm

Simplifying the equation:

5x + 12 = 62

Subtracting 12 from both sides:

5x = 50

Dividing both sides by 5:

x = 10

Therefore, the length of the longest side of the triangle is 2x + 12, which is:

2(10) + 12 = 20 + 12 = 32 cm.

So, the length of the longest side of the triangle is 32 cm.

To find the length of the longest side of the triangle, we need to first establish a system of equations based on the given information.

Let's denote the length of the first side as x cm.
According to the given information, the second side is twice as long as the first side, so its length is 2x cm.
The third side is 12 cm longer than the second side, making its length 2x + 12 cm.

The perimeter of a triangle is the sum of the lengths of all three sides, so we can write the equation:
x + 2x + (2x + 12) = 62

Simplifying the equation:
5x + 12 = 62

Subtracting 12 from both sides:
5x = 50

Dividing both sides by 5:
x = 10

Now we can find the length of the longest side by substituting the value of x into our expression:
2x + 12 = 2(10) + 12 = 20 + 12 = 32 cm

Therefore, the length of the longest side of the triangle is 32 cm.

Let x = first side, then 2x = second side and 2x + 12 is third side. They should add to 62.

Solve for x.