Answers:
- x = 7
- Area of shaded region = 162 square units
You may need to leave off the "square units" portion.
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Explanation:
For now, ignore the smaller rectangle and its dimensions. The larger rectangle has sides 3x and x+5, which I'll call the length and width.
L = 3x
W = x+5
The perimeter of any rectangle is P = 2(L+W). Plug in those values of L and W, and also the given perimeter P = 66. Isolate x.
P = 2(L+W)
2(L+W) = P
2(3x+x+5) = 66
2(4x+5) = 66
8x+10 = 66
8x = 66-10
8x = 56
x = 56/8
x = 7
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Now that we know x, we can find the area of the rectangles.
As you probably can guess, the shaded region is the difference of the two areas.
A = area of larger rectangle
A = (length)*(width)
A = (3x)*(x+5)
A = (3*7)*(7+5)
A = 252
B = area of smaller rectangle
B = (x+3)*(x+2)
B = (7+3)*(7+2)
B = 90
C = area of shaded region
C = A - B
C = 252 - 90
C = 162 square units is the area of the shaded region.
