Question

melissa wants to paint a rectangular region of a wall with one layer of paint. she has 28 yd of tape to tape around the border of the region she paints. she is considering three regions with widths of 5 yd, 6 yd, and 7 yd.
answer the questions below to find which of these regions would require the most paint.
(a) fill in the table to find the length and the area for each region.
(b) which of these regions would require the most paint?
region #1 region #2 region #3

Explanation:

Step1: Find the formula for length

The perimeter of a rectangle is \(P = 2(l + w)\). Given \(P=28\) yd. So, \(28 = 2(l + w)\), then \(l + w=14\), and \(l = 14 - w\).

Step2: Calculate length and area for Region #1

For Region #1, \(w = 5\) yd.
Length: \(l=14 - 5=9\) yd.
Area: \(A=l\times w=9\times5 = 45\) \(yd^{2}\).

Step3: Calculate length and area for Region #2

For Region #2, \(w = 6\) yd.
Length: \(l=14 - 6 = 8\) yd.
Area: \(A=l\times w=8\times6=48\) \(yd^{2}\).

Step4: Calculate length and area for Region #3

For Region #3, \(w = 7\) yd.
Length: \(l=14 - 7=7\) yd.
Area: \(A=l\times w=7\times7 = 49\) \(yd^{2}\).

Answer:

(a)

Region	Width	Length	Area
Region #2	\(6\) yd	\(8\) yd	\(48\) \(yd^{2}\)
Region #3	\(7\) yd	\(7\) yd	\(49\) \(yd^{2}\)

(b) Region #3