Final answer:
The lengths of the sides of the triangle with a 48 cm perimeter and the sides in a 3:4:5 ratio are 12 cm, 16 cm, and 20 cm.
Step-by-step explanation:
To find the lengths of the sides of a triangle with a given perimeter and side length ratio, we can use the concept of ratios and proportions. The sides of the triangle are in the ratio 3:4:5, which means that if we divide the perimeter of the triangle by the sum of the ratio numbers, we can find the length of one part. Then, we can multiply the length of one part by each ratio number to get the lengths of the respective sides.
First, we add the numbers in the ratio 3 + 4 + 5 = 12. We then divide the total perimeter by this sum: 48 ÷ 12 = 4. This means that one part is equal to 4 centimeters. To find the lengths of the sides, we multiply 4 by each of the ratio numbers: 3 × 4 = 12 cm, 4 × 4 = 16 cm, and 5 × 4 = 20 cm.
So, the lengths of the sides of the triangle are 12 cm, 16 cm, and 20 cm, which corresponds to option C.