Question

The rectangle shown below has an area of 4(x+3) square units.
A. Use the distributive property to write an equivalent expression for the rectangle's are.
B. If both of the dimensions of the original rectangle are doubled, what is the area of the new rectangle in terms of x?
C. What is the ratio of the area of the new larger rectangle from B to the area of the original rectangle if the value of x is 7?
D. If the dimensions of the original rectangle are halved, what is the ratio of the area of the new rectangle to the area of the original rectangle?

Answer 1

Answer:

  A.  4x +12

  B.  16x +48

  C.  4

  D.  1/4

Step-by-step explanation:

A. To eliminate parentheses, multiply each term inside by the factor outside.

  4(x +3) = 4x +12

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B. If you like, you can assume the original dimensions are 4 and (x+3). Doubling them makes them 8 and (2x+6). The new area is ...

  8(2x+6) = 16x +48

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C. The value of x is irrelevant. The new area is 2² = 4 times the original

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D. The new area is (1/2)² = 1/4 times the original.

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Additional comment

The area of a rectangle is the product of length and width:

  A = LW

Doubling each of these makes the area be ...

  A' = (2L)(2W) = 4(LW) = 4A

That is, the new area is the original multiplied by the square of the scale factor.