Final answer:
To find the longest side of the triangle, the value of x is determined by using the equation for the perimeter and substituting the given perimeter value. After solving, x is found to be 6 cm, making the longest side of the triangle, which is 2x, equal to 12 cm.
Step-by-step explanation:
To find the length of the longest side of a triangle with sides x, 2x, and x + 5 where the perimeter is 29 cm, we first need to write down the equation that represents the perimeter of the triangle. The perimeter P is the sum of its sides, so we get the equation:
P = x + 2x + (x + 5)
Given that the perimeter P is 29 cm, we substitute and have:
29 = x + 2x + (x + 5)
Combining like terms gives us:
29 = 4x + 5
To find the value of x, we subtract 5 from both sides:
24 = 4x
x = 6
Now that we have the value of x, we can determine the lengths of the sides. The longest side is 2x, so to find its length we simply multiply our value of x by 2:
Longest side = 2x = 2(6) = 12 cm
So, the length of the longest side of the triangle is 12 cm.