The diagram shows the floor plan of a storage facility. All dimensions are given in feet. Which expression represents the area of the storage facility in square feet?

A. 16x^2-16

B. 20x^2+36x-16

C. 20x^2-4x-16

D. 9x^2-16

Please help, thank you

Question

15-02-2020
Mathematics

contestada

The diagram shows the floor plan of a storage facility. All dimensions are given in feet. Which expression represents the area of the storage facility in square feet?

A. 16x^2-16

B. 20x^2+36x-16

C. 20x^2-4x-16

D. 9x^2-16

Please help, thank you

Respuesta :

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SaniShahbaz SaniShahbaz · Answer 1 · 2020-02-21T02:11:31+01:00

Note: As you may have unintentionally missed to add the diagram. After a little research, I was able to find the diagram. I have attached the diagram, based on which I am solving which anyways would clear your concepts.

Answer:

The area of the storage facility is [tex]20x^2-4x-16\:\:square\:feet[/tex].

Step-by-step explanation:

From the attached diagram, it is clear that

The length of the rectangle [tex]=5x + 4[/tex]

The width of the rectangle [tex]= 4x - 4[/tex]

The area of the storage facility in square feet can be calculated by finding the area of rectangle.

So, using the area of rectangle formula

[tex]A = lw[/tex]

[tex]=\:\left(5x+4\right)\left(4x-4\right)[/tex]

[tex]\mathrm{Apply\:FOIL\:method}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd[/tex]

[tex]a=5x,\:b=4,\:c=4x,\:d=-4[/tex]

[tex]=5x\cdot \:4x+5x\left(-4\right)+4\cdot \:4x+4\left(-4\right)[/tex]

[tex]=5\cdot \:4xx-5\cdot \:4x+4\cdot \:4x-4\cdot \:4[/tex]

[tex]=20x^2-4x-16[/tex]

Therefore, the area of the storage facility is [tex]20x^2-4x-16\:\:square\:feet[/tex].

Keywords: rectangle, area

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The diagram shows the floor plan of a storage facility. All dimensions are given in feet. Which expression represents the area of the storage facility in square feet?A. 16x^2-16B. 20x^2+36x-16C. 20x^2-4x-16D. 9x^2-16Please help, thank you

Respuesta :

Otras preguntas

The diagram shows the floor plan of a storage facility. All dimensions are given in feet. Which expression represents the area of the storage facility in square feet?

A. 16x^2-16

B. 20x^2+36x-16

C. 20x^2-4x-16

D. 9x^2-16

Please help, thank you