There are two buildings that you want to have in the amusement park, but the size hasn’t been determined yet. although you don’t know the specific dimensions, you do know the relationships between the sides. the first is the rectangular gift shop. you know that the length will be 20x+24 feet and the width will be 36-20 feet. a) write the expression that represents the area of the gift shop, in terms of x. b) write the expression that represents the perimeter of the gift shop, in terms of x. c) if the perimeter is going to be 176 feet, what are the dimensions of the building?

We have that
the length will be 20x+24 feet
and 
the width will be 36x-20 feet

Part a)  Write the expression that represents the area of the gift shop, in terms of x

we know that
area of a rectangle A=lenght*width
A=(20x+24)*(36x-20)
A=720x²-400x+864x-480
A=720x²+464x-480

the answer part a) is
the expression that represents the area of the gift shop, in terms of x. is
A=720x²+464x-480

Part b) Write the expression that represents the perimeter of the gift shop, in terms of x

the perimeter of a rectangle P=2*[length+width]
P=2*[(20x+24)+(36x-20)]
P=2*[56x+4]
P=112x+8

the answer part b) is
the expression that represents the perimeter of the gift shop, in terms of x is
P=112x+8

Part c) If the perimeter is going to be 176 feet, what are the dimensions of the building?
P=176 ft
P=112x+8
112x+8=176
112x=176-8
x=168/112
x=1.5 ft
length=(20x+24)> 20*1.5+24> 54 ft
width=36x-20> 36*1.5-20> 34 ft

the answer part c) is
length is 54 ft
width is 34 ft

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