Final answer:
The lengths of the sides of the triangle with a perimeter of 120 mm and side ratio of 4:5:3 are 40 mm, 50 mm, and 30 mm.
Step-by-step explanation:
To find the lengths of the sides of a triangle with a given perimeter and sides in the ratio of 4:5:3, one must use the concept of ratios and the definition of perimeter. Let the common factor by which the sides are multiplied be x. Therefore, the sides can be represented as 4x, 5x, and 3x. The perimeter is the sum of these sides; hence, 4x + 5x + 3x = 120 mm. Combining like terms gives 12x = 120 mm, and dividing by 12 gives x = 10 mm. The lengths of the sides are now obtained by multiplying the common factor x with the respective ratios. The sides are 4x = 40 mm, 5x = 50 mm, and 3x = 30 mm.