Final answer:
By setting up an equation for the perimeter of the triangle and solving for x, the lengths of the sides are determined to be 9 cm, 15 cm, and 17 cm.
Step-by-step explanation:
To find the lengths of each side of a triangle with sides described as x+5, 2x+7, and 4x+1 and a given perimeter of 41 cm, we set up the equation representing the perimeter:
x + 5 + 2x + 7 + 4x + 1 = 41
Combining like terms, we have:
7x + 13 = 41
Subtracting 13 from both sides gives us:
7x = 28
Dividing both sides by 7 yields:
x = 4
Now, we substitute x = 4 back into the expressions for each side to find their lengths:
The first side: x + 5 becomes 4 + 5 = 9 cm
The second side: 2x + 7 becomes 2(4) + 7 = 15 cm
The third side: 4x + 1 becomes 4(4) + 1 = 17 cm
Therefore, the lengths of the sides of the triangle are 9 cm, 15 cm, and 17 cm.