Width is 6; Length is 24

Explanation:

Key points:

Rectangle shape

Area

→

144

f

t

2

Width =

length

4

'

Let the area be

A

=

144

Let the width be

W

Let the length be

L

Explanation:

Key points:

Rectangle shape

Area

→

144

f

t

2

Width =

length

4

'

Let the area be

A

=

144

Let the width be

W

Let the length be

L

The area of a rectangle is the multiplication of its width times its length, that is:

area = width*length

We have to write as an equation the information about the relationship between the width and the length, they say the width is 1/4 of the lenght, this is:

width = lenght/4

now we substitute the data we have:

area = width*length

144 = (length/4)*length

length^2 = 4*144 = 576

the length is raised to the second power because we had to multiply length*length, so to solve the last equation we had to take the square root to both sides:

length = √576

length = 24

so the length of the banner is 24 feet, and we know that:

width = lenght/4

width = 24/4

width = 6

so the width is 6 feet

area = width*length

We have to write as an equation the information about the relationship between the width and the length, they say the width is 1/4 of the lenght, this is:

width = lenght/4

now we substitute the data we have:

area = width*length

144 = (length/4)*length

length^2 = 4*144 = 576

the length is raised to the second power because we had to multiply length*length, so to solve the last equation we had to take the square root to both sides:

length = √576

length = 24

so the length of the banner is 24 feet, and we know that:

width = lenght/4

width = 24/4

width = 6

so the width is 6 feet

The answer to your question is width = 6 ft; length = 24 ft

Step-by-step explanation:

Data

Area = 144 ft²

width = w

length = l

The width is 1/4 of the length

Formula

Area = width x length = w x l

Length = 4 width l = 4w

Process

1.- Substitute length in the first equation

Area = w(4w)

Simplify

Area = 4w²

2.- Solve for w

w =

Substitution

w =

Simplification

w =

Result

w = 6 ft

3.- Find l

l = 4(6)

l = 24 ft

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