Question

Kiyo is designing a rectangular garden with a 2-ft wide path all the way around it.

The length of the garden is 3 times as long as the width. Kiyo models the area of
his garden and the path with the equation f(x) = (x + 2)(3x + 2). Explain Kiyo’s error.

Answer 1

Answer: Kiyo only accounted for one side of the path when creating his equation. There are 2 feet of path on each side of the garden, meaning there should be 4 extra feet added to each expression multiplied.

Explanation:

The rectangular path surrounding the garden is 2 feet on each side.

The length of the garden is represented by 3x, but when the length of the path is included, there is 2 feet of path on the left of the garden and 2 feet of path on the right.

Due to this, Kiyo made the mistake of only including 2 feet instead of the full 4 of the path by only accounting for one side of the path.

The correct equation is:

`f(x) = (x+4)(3x+4)`

Answer 2

38 ft

Explanation:

Let x and (3x+2) represent the width and length respectively:

L + W = P/2 = 100/2 = 50

(3x+2) + x = 50

4x = 48

x = 12ft, the width, the length is 38ft