Final answer:
The width of the rectangular snow fort, given that the perimeter is 20x - 50 and the length is 5x - 13, is 5x - 12.
Step-by-step explanation:
The student is asking for the width of a rectangular snow fort, given that the perimeter is 20x - 50 and the length is 5x - 13. To find the width, we need to use the formula for the perimeter of a rectangle, which is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
- First, substitute the known perimeter and length into the formula: 20x - 50 = 2((5x - 13) + w).
- Simplify and solve for w: 20x - 50 = 2(5x - 13) + 2w.
- Distribute the 2: 20x - 50 = 10x - 26 + 2w.
- Now, move the terms involving x to one side: 20x - 10x = 2w + 26 - 50.
- Simplify further: 10x = 2w - 24.
- Finally, divide both sides by 2 to find w: w = 5x - 12.
Therefore, the measurement of the width of the snow fort is 5x - 12.