Question

The perimeter of a certain scalene triangle is 100 inches. The side lengths of the triangle are represented by 5x, 3x + 30, and, 2x + 10, respectively. What is the length, in inches, of the longest side of the triangle?

Answer 1

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.