the ratio of the measures of the sides of a triangle is 10:15:6. if the perimeter of the triangle is 217 meters find the shortest side

Answer 1

Perimeter = Side1+Side2+Side3

217=10x+15x+6x Combine like terms

217=31x Divide both sides by 31

x=7

For the shortest side, 6x = 6(7) = 42 m

Answer 2

Hi Liyah S

You can apply ratio and proportion to your given values

You are given a total 217

Your are given the ratio of the sides relative to the total

Note the ratio 10:15:6 is in reduced terms

10 + 15 + 6 = 31 is the total for the small scale use this to calculate the sides for the given total as follows:

Let x = smallest side

Let y = next side

Let z = longest side

6/31 = x/217

Cross multiply

x = 6(217)/31

x = 42

Do the same for the other sides

10/31 = y/217

y = 10(217)/31

y = 70

15/31 = z/217

z = 15(217)/31

z = 105

You can check both the total and ratio

105 + 70 + 42 =217

Keeping in mind the order of the ratio stated in your problem

70:105:42

The numbers above need to be in lowest terms, so they need a common factor, that factor is 7

70/7=10

105/7=15

42/7 = 6

So 70:105:42 in lowest terms is 10:15:6

Of course, there are other ways to do the problem a quick comparison of the totals followed by some multiplication of the ratios should work as well maybe you can try that.

I hope you find this useful if you have any questions please send me an email.

Answer 3

10:15:6 ratio of sides summing to 217

10+15+6 = 31. 217/31 = 7

actual sides are

7(10), 7(15) and 7(6), 7x6 = 42 meters = the shortest side