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A blackboard has an area of 28 ft2 and a perimeter of 22 ft. What are the dimensions of the board?

 May 13, 2020
 #1
avatar+902 
-2

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

 May 13, 2020
 #2
avatar+111433 
+2

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

 

 

cool cool cool

 May 13, 2020

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