Question

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

Answer 1

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 $20x^2-4x-16\:\:square\:feet$.

Step-by-step explanation:

From the attached diagram, it is clear that

• The length of the rectangle  $=5x + 4$

• The width of the rectangle $= 4x - 4$

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

                $A = lw$

                    $=\:\left(5x+4\right)\left(4x-4\right)$

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

$a=5x,\:b=4,\:c=4x,\:d=-4$

                        $=5x\cdot \:4x+5x\left(-4\right)+4\cdot \:4x+4\left(-4\right)$

                        $=5\cdot \:4xx-5\cdot \:4x+4\cdot \:4x-4\cdot \:4$

                        $=20x^2-4x-16$  

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

Keywords: rectangle, area

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