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?

Answer 1

To solve for the length and width of the rectangular garden, create two equations based on the given perimeter and the relationship between length and width, then substitute and solve.

Step-by-step explanation:

The question involves finding the length and width of a rectangular garden with a given perimeter and a relationship between the length and width. The perimeter of a rectangle is the sum of all its sides, which can be represented by the formula 2 × (length + width). The problem states that the perimeter is 56 feet and that the length (L) is eight feet less than twice the width (W). This gives us two equations: 2L + 2W = 56 and L = 2W - 8. We can substitute the expression for L from the second equation into the first one to find W. Once we find W, we can easily calculate L.

Steps to Solve

1. Write the first equation for the perimeter: 2L + 2W = 56.
2. Write the second equation relating length and width: L = 2W - 8.
3. Substitute the expression for L into the perimeter equation: 2(2W - 8) + 2W = 56.
4. Simplify and solve for W.
5. Once W is found, use it to calculate L using the second equation.

By solving these equations, we find the width and length of the garden.