Question

A triangle has side lengths of left parenthesis, 7, point, 9, a, plus, 8, point, 8, b, right parenthesis(7.9a+8.8b) centimeters, left parenthesis, 6, point, 2, a, plus, 1, point, 5, c, right parenthesis(6.2a+1.5c) centimeters, and left parenthesis, 4, point, 2, c, plus, 5, point, 9, b, right parenthesis(4.2c+5.9b) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

Answer 1

The perimeter of a triangle is the sum of the lengths of its sides. In this case, the side lengths of the triangle are given as follows:

1. First side: \(7.9a + 8.8b\) centimeters
2. Second side: \(6.2a + 1.5c\) centimeters
3. Third side: \(4.2c + 5.9b\) centimeters

To find the perimeter \(P\), we need to sum these three expressions:

\[ P = (7.9a + 8.8b) + (6.2a + 1.5c) + (4.2c + 5.9b) \]

Now, we can combine like terms:

1. Combine the terms involving \(a\):

   • \(7.9a + 6.2a = (7.9 + 6.2)a = 14.1a\)

2. Combine the terms involving \(b\):

   • \(8.8b + 5.9b = (8.8 + 5.9)b = 14.7b\)

3. Combine the terms involving \(c\):

   • \(1.5c + 4.2c = (1.5 + 4.2)c = 5.7c\)

Putting it all together, the expression for the perimeter \(P\) is:

\[ P = 14.1a + 14.7b + 5.7c \]

Therefore, the expression that represents the perimeter of the triangle is:

\[ \boxed{14.1a + 14.7b + 5.7c} \]