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.

Step-by-step 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:

Cross multiply to get

30a = 225 and

a = 7.5

Cross multiply to get

30b = 540 and

b = 18

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