Final answer:
To find the dimensions of the triangle with a given perimeter, we used algebra to represent the relationships between the sides. We found that the three sides are 7 inches, 8 inches, and 11 inches respectively.
Step-by-step explanation:
To find the dimensions of the sides of the triangle when given the perimeter and the relationships between the sides, let's denote the shortest side as x inches. According to the question, one side is six less than twice the shortest side, which can be represented as 2x - 6 inches. The other side is four more than the shortest side, written as x + 4 inches. The perimeter of a triangle is the sum of the lengths of all three sides, which in this case is 26 inches.
To find the dimensions:
- Write an equation representing the perimeter: x + (2x - 6) + (x + 4) = 26.
- Combine like terms: 4x - 2 = 26.
- Solve for x: 4x = 28, hence x = 7 inches.
- Now, calculate the lengths of the other sides: 2x - 6 inches and x + 4 inches.
- Substitute the value of x to get the dimensions of the other sides: One side is 2(7) - 6 = 8 inches and the other side is 7 + 4 = 11 inches.
Therefore, the dimensions of the three sides of the triangle are 7 inches, 8 inches, and 11 inches.