Asmall plane is flying a banner in the shape of a rectangle. the area of the banner is 144 square feet . the width of the banner is 1/4 the length of the banner. what are the dimensions of the banner?

Answers

X * (x/4) = 144

(x^2)/4 = 144

x^2 = 144*4

x = 24

Dimensions: 6 * 24
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
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
The answer to that math problem is 144 by 36 (it has to be 20 characters or more)
6 feet by 24 feet. 6 is 1/4th of 24, and 6 multiplied by 24 is 144.

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 = \sqrt{\frac{Area}{4}}

Substitution

                      w = \sqrt{\frac{144}{4}}

Simplification

                      w = \sqrt{36}

Result

                      w = 6 ft

3.- Find l

                       l = 4(6)

                       l = 24 ft



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