Question

The lengths of the sides of a triangle are in the ratio 5:12:13. The perimeter is 45 miles. Find the length of the sides.

Answer 1

Explanation:

The perimeter of any object is found by adding all the lengths of the sides together. Our perimeter is 45. Therefore, side a + side b + side c = 45. We know that the ratio is 5:12:13. We can either reduce these down by a factor of 5 or we can leave it the way it is and work from there. Either way you get the same answer. Let's leave it.

The sum of the ratios is 5 + 12 + 13 = 30. We have 2 equations now:

a + b + c = 45

5 + 12 + 13 = 30

Let's say for the sake of argument that a is to 5 as b is to 12 as c is to 13 as 45 is to 30. We can set up proportions to solve for the lengths:

`(5)/(a)=(30)/(45)`

Cross multiply to get

30a = 225 and

a = 7.5

`(12)/(b) =(30)/(45)`

Cross multiply to get

30b = 540 and

b = 18

`(13)/(c) =(30)/(45)`

Cross multiply to get

30c = 585 and

c = 19.5

Let's add them together to make sure we get 45 as a sum:

7.5 + 18 + 19.5 = 45