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21. You are making a rectangular poster to advertise a school fundraiser. You
want the poster to be twice as long as it is wide. Let w represent the width
(in meters) of the poster.
a. Write and simplify an expression in terms of w for the perimeter of
the poster
b. Write and simplify an expression in terms of w for the area of the poster.
c. Complete the table.
Width (meters)
Perimeter (meters)
Area (square meters)
?
?
?
?
| 3
?
?
| 4
?
?
d. Which width given in the table allows for the most area while not
exceeding a perimeter of 20 meters?​

Respuesta :

lucic

The simplified expression for perimeter is 6w, and for area is 2w². 3 meters of a width will allow the most area while not exceeding a perimeter of 20 meters.

Step-by-step explanation:

Let w represent the width of the poster then,

The length of the poster is twice as long as its width, to mean the length is 2w

Perimeter is the distance around the figure. Your figure is a rectangle with sides width, w and length 2w;

Perimeter formula is = 2(l+w) where l is length and w is with

P=2(2w+w) = 2(3w) = 6w meters

Area is given by the product of length and width of the figure

Area=l*w

A=2w*w= 2w²

The table will be;

Width in (m)       Perimeter=6w in (m)           Area (2w²) in m²

3                          6*3= 18                                   2*3²=2*9=18

4                          6*4=24                                  2*4²=2*16=32

Width 3 allows for the most area while not exceeding a perimeter of 20 meters.

Learn More

Area of a rectangle figure : https://brainly.com/question/9624810

Keywords : rectangular poster, perimeter, area, expression

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