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 <span>the length will be 20x+24 feet and </span><span>the width will be 36x-20 feet
Part a) </span><span> 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=720x</span>²-400x+864x-480 A=720x²+464x-480
the answer part a) is <span>the expression that represents the area of the gift shop, in terms of x. is </span>A=720x²+464x-480
Part b) <span>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 </span><span>the expression that represents the perimeter of the gift shop, in terms of x is </span>P=112x+8
Part c) <span>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</span>
