The lengths of the sides of a triangle have a ratio of 3:6:8. The perimeter is 510cm; Find the lengths of all sides

Step-by-step explanation:

Ratios exist because the constant of variation, k, is the same number multiplied into each side to keep them all proportionate to one another.

The question is basically asking us to find the value of k that not only keeps these sides in proportion to one another, but also has the perimeter come to 510. Because k is the same number and is our unknown, we can multiply each side by k and set the sum of the sides equal to 510.

3k + 6k + 8k = 510 and

17k = 510 so

k = 30

That means the lengths of 3 (30) = 90, 6 (30) = 180, and 8 (30) = 240 are the lengths of the sides. 90 + 180 + 240 = 510