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A picture frame consists of two rectangular strips of wood, each having a width of 1 inch on all sides. If the area of the inner light gray strip is 100 \(\text{in}^2\) , then compute the area of the outer dark gray strip in square inches.

 

Lightning  Oct 14, 2018
 #1
avatar+90968 
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See...my  corrected answer under your orginal post, Lightning...

 

 

cool cool cool

CPhill  Oct 14, 2018
 #2
avatar+90968 
+1

Let me do this one algebraically

 

Let the "white"  area in the middle have sides of x and y

 

So..it's area  = xy

 

Note that the light gray strip  plus the white area  will   have dimensions of  (x +2) and (y + 2)

[ We are adding 1 inch to each side of the white area  ]

 

So....this area  minus the white area   =   area of  light grey strip

Algebraically, we have

 

(x + 2) (y + 2)  - xy = 100

 

xy + 2(x + y) + 4  - xy  = 100

 

2(x+ y) + 4 = 100

 

2(x + y) = 96

 

x + y =  48

 

Now the total arra of the figure can be represented as  ( x + 4) (y + 4)

[ We are adding 2 inches to every side of the white area ]

 

So

 

Total area  -  area of light grey strip -  white area  = area of dark grey strip

 

(x + 4) (y + 4)  - 100 - xy  =

 

xy + 4(x + y) + 16  - 100  - xy  =

 

4 (x + y)  + 16  - 100  =

 

4(48)  + 16  - 100  = 

 

192  + 16  - 100  =

 

208  - 100  =

 

108 in^2  = area of dark grey strip 

 

 

cool cool cool

CPhill  Oct 15, 2018

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