Question

raina wants to paint a rectangular region of a wall with one layer of paint. she has enough paint to cover a region that is ( 16 mathrm{~m}^{2} ). before painting, she wants to put a strip of tape around the border of the region. she is considering three regions with lengths of ( 1 mathrm{~m}, 4 mathrm{~m} ), and ( 8 mathrm{~m} ). answer the questions below to find which of these regions would require the least tape. (a) fill in the table to find the width and the perimeter for each region. (b) which of these regions would require the least tape? region #1 region #2 region #3

Explanation:

Step1: Find the width for each region

The area formula for a rectangle is \(A = l\times w\). So \(w=\frac{A}{l}\).
For Region #1: \(l = 1m\), \(A=16m^{2}\), then \(w=\frac{16}{1}=16m\)
For Region #2: \(l = 4m\), \(A = 16m^{2}\), then \(w=\frac{16}{4}=4m\)
For Region #3: \(l = 8m\), \(A=16m^{2}\), then \(w=\frac{16}{8}=2m\)

Step2: Find the perimeter for each region

The perimeter formula for a rectangle is \(P=2(l + w)\)
For Region #1: \(l = 1m\), \(w = 16m\), \(P=2(1 + 16)=2\times17 = 34m\)
For Region #2: \(l = 4m\), \(w = 4m\), \(P=2(4 + 4)=2\times8=16m\)
For Region #3: \(l = 8m\), \(w = 2m\), \(P=2(8 + 2)=2\times10 = 20m\)

Answer:

(a)

Length	Width	Perimeter
4m	4m	16m
8m	2m	20m

(b) Region #2