Question

A rectangular garden has a perimeter of 56 feet. If the length is eight less than twice the width, what is the length and width of the garden?

a) Length = 20 feet, Width = 16 feet
b) Length = 18 feet, Width = 10 feet
c) Length = 24 feet, Width = 14 feet
d) Length = 22 feet, Width = 12 feet

Answer 1

To find the length and width of the garden, we can set up a system of equations using the given information. Solving the system will give us the values of the width and length. Length = 22 feet, Width = 12 feet. So, the correct answer is option d

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let the width of the garden be w feet, then the length of the garden is 2w - 8 feet.

The perimeter of a rectangle is given by the formula 2(length + width).

We can set up the equation 2(2w - 8 + w) = 56 and solve it to find the value of w.

Once we find the value of w, we can substitute it back into the formula 2w - 8 to find the length of the garden.

1. Let's solve the equation: 2(2w - 8 + w) = 56
2. Expanding the brackets gives: 2(3w - 8) = 56
3. Simplifying further gives: 6w - 16 = 56
4. Adding 16 to both sides gives: 6w = 72
5. Dividing both sides by 6 gives: w = 12
6. Substituting the value of w = 12 back into 2w - 8 gives: 2(12) - 8 = 24 - 8 = 16

Therefore, the length of the garden is 16 feet and the width of the garden is 12 feet.

So, the correct answer is option d) Length = 22 feet, Width = 12 feet.