Final answer:
The width of the yard is 40 feet, and the length is 50 feet, calculated by using two equations to represent the given perimeter and relationship between length and width.
Step-by-step explanation:
To find the length and width of a rectangular yard with a perimeter of 180 feet, where the length is 10 feet longer than the width, we can set up two equations based on the given information. Let w represent the width and l represent the length.
- Perimeter equation: 2w + 2l = 180
- Length equation: l = w + 10
Substituting the second equation into the first gives us 2w + 2(w + 10) = 180. Simplifying this, we get 2w + 2w + 20 = 180, which leads to 4w = 160, and dividing both sides by 4, we find w = 40. Now we can use this value to find the length, l = w + 10, so l = 40 + 10 which equals 50. Therefore, the dimensions of the yard are 50 feet by 40 feet.