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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.

Oct 14, 2018

#1
+103049
0

Oct 14, 2018
#2
+103049
+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

Oct 15, 2018