A rectangular sign had a perimeter of 44 feet and a length of 14 feet. A designer shortened the length so that the sign became a square with the same width as the old sign. What was the area of the new sign?

A.

64 ft2

B.

196 ft2

C.

112 ft2

D.

256 ft2

Question

A rectangular sign had a perimeter of 44 feet and a length of 14 feet. A designer shortened the length so that the sign became a square with the same width as the old sign. What was the area of the new sign? 	
	
 
A.
	

64 ft2
	
 
B.
	

196 ft2
	
 
C.
	

112 ft2
	
 
D.
	

256 ft2

anonymous · Answer

A rectangular sign had a perimeter of 44 feet and a length of 14 feet. A designer shortened the length so that the sign became a square with the same width as the old sign. What was the area of the new sign? 	
	
 
A.
	

64 ft2
	
 
B.
	

196 ft2
	
 
C.
	

112 ft2
	
 
D.
	

256 ft2

anonymous · Answer

a length of 14 feet and a perimeter of 44 feet means that your width can be obtained with a perimeter function:
perimeter is a function of length and width p(l, w)
2l + 2w = p(l, w)
2(14) + 2w = 44 = p(14, w)
28 + 2w = 44
2w = 44 - 28
2w = 16
w = 8

so if you have a new square with a width of 8 the value of its area is the function:
a(w) = w^2
a(8) = (8)^2
a(8) = 64
so your area will be 64 ft squared