The ratio of the measures of three sides of a triangle are 1/2:1/3:1/5, and its perimeter is 6.2 centimeters. find the measure of each side of the triangle
sides are 1/2 x , 1/5 x , 1/3 x
perimeter = (1/2 + 1/5 + 1/3 ) x = 6.2
(15/30 + 6/30 + 10/30 ) x = 6.2
31x/30 = 6.2
x = 6
so 3 , 6/5, 2
To find the measure of each side of the triangle, we need to first determine the actual values of the ratios given.
Let's assume that the measures of the three sides of the triangle are (1/2)x, (1/3)x, and (1/5)x, where x is the common multiplier.
Given that the perimeter of the triangle is 6.2 centimeters, we can set up the equation:
(1/2)x + (1/3)x + (1/5)x = 6.2
To solve this equation, we need to find a common denominator. In this case, the least common denominator is 30. So, let's multiply each fraction by the appropriate factor to get the equation:
(15/30)x + (10/30)x + (6/30)x = 6.2
Now, we can combine the terms:
(31/30)x = 6.2
To isolate x, we will multiply both sides of the equation by 30/31:
x = (6.2 * 30) / 31
x ≈ 5.9677
Now that we have found the value of x, we can substitute it back into the original ratios to find the measure of each side:
(1/2)x ≈ (1/2) * 5.9677 ≈ 2.9839
(1/3)x ≈ (1/3) * 5.9677 ≈ 1.9893
(1/5)x ≈ (1/5) * 5.9677 ≈ 1.1936
Therefore, the measure of each side of the triangle is approximately 2.9839 centimeters, 1.9893 centimeters, and 1.1936 centimeters.