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1.
The diagram below shows a composite shape formed by joining two rectangles.
4 cm
I
xcm
12 cm
(x + 2)cm
Diagram not drawn to scale
The area of the larger rectangle is 4 times the area of the smaller rectangle.
Calculate the dimensions of the smaller rectangle.
You must justify any decisions that you make.​

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Answer:

  24 cm^2

Step-by-step explanation:

The larger rectangle has dimensions in cm of 12 by (4+x). The smaller rectangle has dimensions of (x+2) by x. The area of the larger is 4 times the smaller, so ...

  12(4+x) = 4(x)(x+2)

  3(4+x) = x(x+2) . . . . . . divide by 4

  x^2 +2x -3x -12 = 0 . . . eliminate parentheses, subtract 3(4+x)

  (x -4)(x +3) = 0 . . . . . . . factor

The positive solution is x = 4, so the area of the smaller rectangle is ...

  x(x+2) = 4(4+2) = 24 . . . cm^2

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