Question

Set up a system of equations needed to solve the problem. Solve by the method of your choice. The perimeter of a rectangular field is 76 ft. The length is 12 ft longer than the width. Find the field’s dimensions.""

Answer 1

To solve for the dimensions of the rectangular field, a system of equations is created from the perimeter and the relationship between length and width. Solving the system reveals that the width is 13 ft and the length is 25 ft.

Step-by-step explanation:

To find the dimensions of a rectangular field where the perimeter is 76 ft and the length is 12 ft longer than the width, we need to set up a system of equations. Let W represent the width and L represent the length of the field. The system of equations is then:

• 2L + 2W = 76 (perimeter equation)
• L = W + 12 (relationship between length and width)

We can substitute the second equation into the first to find W:

• 2(W + 12) + 2W = 76
• 2W + 24 + 2W = 76
• 4W + 24 = 76
• 4W = 76 - 24
• 4W = 52
• W = 13 ft

Now we plug this value back into L = W + 12 to find the length:

• L = 13 + 12
• L = 25 ft

Therefore, the dimensions of the field are a width of 13 ft and a length of 25 ft.