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

Step-by-step 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

g = (2, 2)

step-by-step explanation:

given the ratio is 1 : 1 then f is the midpoint of eg

let the coordinates of g = (x, y)

using the midpoint formula

(0 + x) = 1 ( multiply both sides by 2 )

0 + x = 2 ⇒ x = 2

similarly

(4 + y) = 3 ( multiply both sides by 2 )

4 + y = 6 ( subtract 4 from both sides )

y = 2

coordinates of g = (2, 2)