A blackboard has an area of 28 ft2 and a perimeter of 22 ft. What are the dimensions of the board?
+1005 l*w = 28
2(l+w) = 22
so l+w = 11
factor pairs of 28:
1,28
2,14
4,7
4+7 = 11!
Dimensions: 4*7
+128460 Area = LW = 28
Perimeter = 2(W + L)
So we have this
28 = LW (1)
22 = 2(W + L) divide by 2 on both sides
11= L + W subtract W from both sides
11 - W = L (2)
Sub (2) into (1) for L and we have that
28 = (11 - W) * W simplify
28 = 11W - W^2 rearrange as
W^2 - 11W + 28 = 0 factor
(W -7) ( W - 4) = 0
Setting each factor to 0 and solving for W will give us the dimensions
W = 7 or W = 4
So....the dimensions are 7 ft x 4 ft
