Question

A triangle has side lengths of (6.5r + 4.2) centimeters, (2.4r – 9.8) centimeters, and (9.5s - 5.2) centimeters. Which expression represents the perimeter, in centimeters, of the triangle?

A. 18.4r + 6.5s - 10.8 centimeters
B. 18.4r - 10.8s - 10.8 centimeters
C. 18.4r - 6.5s + 10.8 centimeters
D. 18.4r + 2.4s - 10.8 centimeters

Answer 1

The perimeter of the triangle with given sides will be the sum of those sides after combining like terms. Upon calculating, we find that the expression for the perimeter is 8.9r + 9.5s - 10.8 centimeters, which does not match any of the answer choices provided.

Step-by-step explanation:

The perimeter of a triangle is given by adding the lengths of all three sides. Given the side lengths of (6.5r + 4.2) centimeters, (2.4r – 9.8) centimeters, and (9.5s - 5.2) centimeters, the expression for the perimeter will be the sum of these three expressions.

Perimeter = (6.5r + 4.2) + (2.4r – 9.8) + (9.5s - 5.2)

Combine like terms to get:

Perimeter = 6.5r + 2.4r + (4.2 - 9.8) + 9.5s - 5.2

Perimeter = 8.9r - 5.6 + 9.5s - 5.2

Perimeter = 8.9r + 9.5s - 10.8 centimeters. This matches none of the provided choices, implying there may be a typo or mistake in the question or answer choices, as s and r are not combined in the provided expression.