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

perimeter function of length and width so p(l, w)
given: p(l, w) = 44
and l = 14
need a function for p in terms of l and w
p(l, w) = 2l + 2w
l = 14 so plug this in
p(14, w) = 2(14) + 2w
p(14, w) = 28 + 2w
also we know p(14, w) = 44 so
44 = 28 + 2w
44 - 28 = 2w
16 = 2w
8 = w
now we want a square with width 8, so square 8
8^2 = 64
area = 64