Final answer:
To find the dimensions of a backyard with a perimeter of 64 meters, where the length is 4 meters less than double the width, a system of equations is set up and solved, revealing that the width is 12 meters and the length is 20 meters.
Step-by-step explanation:
The student has asked to determine the dimensions of a backyard with a given perimeter and a relationship between its length and width. Let's denote the width of the backyard as w and the length as l. According to the question, the perimeter of the backyard is 64 meters and the length is 4 meters less than double the width. The formula for the perimeter of a rectangle is P = 2l + 2w, where P stands for perimeter, l for length, and w for width.
First, let's set up our equations based on the given information:
- l = 2w - 4 (The length is 4 meters less than double the width)
- P = 64 (The total perimeter is 64 meters)
Now, we replace l in the perimeter equation with 2w - 4:
- P = 2(2w - 4) + 2w
- 64 = 4w - 8 + 2w
- 64 = 6w - 8 (Combine like terms)
- w = 12 (Solve for w by adding 8 to both sides and then dividing by 6)
Now that we know the width, we can find the length:
- l = 2(12) - 4
- l = 20 (Double the width and subtract 4)
Therefore, the dimensions of the backyard are 20 meters in length and 12 meters in width.