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

The correct equation that models the area if x(3x) or 3x² where x is the width of the path

Explanation:

Area of a rectangle = Length *Width

Width of the rectangular garden W = 2ft

If the length of the garden is 3 times as long as the width, then length = 3 * width i.e W = 3L

Since Area of the path A = L* W

A = (3W)W

A = 3W²

If the width is the same as x then

Area f(x) = (3x)(x)

According to kyle, the area of his path f(x) = (x + 2)(3x + 2) which is wrong because of kyle addition of 2 to each of the value of the length and width respectively which kyle shouldn't have added any value to the dimension to the garden