Final answer:
To determine the longest side of a scalene triangle with a perimeter of 100 inches and sides 5x, 3x + 30, and 2x + 10, we find x by solving the perimeter equation and then calculate each side length. The longest side is found to be 48 inches.
Step-by-step explanation:
The student's question involves finding the length of the longest side of a scalene triangle with a given perimeter (100 inches) and sides represented by algebraic expressions (5x, 3x + 30, 2x + 10).
The first step is to write the equation for the perimeter: 5x + (3x + 30) + (2x + 10) = 100.
Solving for x gives us the individual side lengths, and we can then determine which is the longest.
After simplifying the equation, we get 10x + 40 = 100, so x = 6.
Plug this back into the expressions for the side lengths to get: 5x = 30 inches, 3x + 30 = 48 inches, and 2x + 10 = 22 inches.
Hence, the longest side is 48 inches long.