Final answer:
To find the measure of each side of the triangle, we calculate the common factor x by dividing the perimeter by the sum of the ratio numbers (21), which gives x ≈ 9.119. Multiplying the ratio numbers 9, 7, and 5 by x gives us the side lengths which are approximately 82.07, 63.83, and 45.60.
Step-by-step explanation:
The student has asked for the measure of each side of a triangle given that the ratio of the sides is 9:7:5 and its perimeter is 191.5. To find the measure of each side, we'll use the concept of ratios and the perimeter.
Step-by-step Solution:
Let the common factor by which each ratio number is to be multiplied to get the lengths of sides be x. So the sides are 9x, 7x, and 5x.
The sum of the sides, which is the perimeter, is given by 9x + 7x + 5x = 191.5.
- Simplifying the equation gives us 21x = 191.5.
- Divide both sides of the equation by 21 to find x:
x = 191.5 / 21. - Calculate the value of x to get x = 9.119.
- Multiply the ratio numbers by x to get the actual lengths: side 1 is 9x = 9(9.119) ≈ 82.07, side 2 is 7x = 7(9.119) ≈ 63.83, and side 3 is 5x = 5(9.119) ≈ 45.60.
Therefore, the measures of the sides of the triangle are approximately 82.07, 63.83, and 45.60.