Question

Carly stated, "All pairs of rectangles are dilations. " Which pair of rectangles would prove that Carly’s statement is incorrect? A rectangle with length 4 and width 2. A rectangle with length 8 and width 4. A rectangle with length 4 and width 2. A rectangle with length 6 and width 3. A rectangle with length 4 and width 3. A rectangle with length 3 and width 2. A rectangle with length 4 and width 3. A rectangle with length 2 and width 1. 5.

Answer 1

Answer:

c

Step-by-step explanation:

Answer 2

The pair of rectangle that will prove Carly's statement incorrect is: Option 3: A rectangle with length 4 and width 3. A rectangle with length 3 and width 2.

How to find if a pair of figure is not dilated version of each other?

Dilation of a figure will leave its sides get scaled (multiplied) by same number.

Thus, suppose if a rectangle is dilated, and its sides were of length = L and width = W, then its dilated version would be having length = Ln, and width = Wn where n is the factor of scaling.

Thus, we get:

$n = \dfrac{Ln}{L} = \dfrac{Wn}{W}\\\\or\\\\\text{Ratios of corresponding dilated sides are equal}$

For the given cases, checking all the given pairs:

• Case 1:  A rectangle with length 4 and width 2. A rectangle with length 8 and width 4.

Getting length to length and width to width ratio:

$\dfrac{L_1}{L_2} = \dfrac{4}{8} = \dfrac{1}{2}\\\\\dfrac{W_1}{W_2} = \dfrac{2}{4} = \dfrac{1}{2}\\\\\\Thus, \dfrac{L_1}{L_2} = \dfrac{W_1}{W_2}$

Pair given are dilated version of each other.

• Case 2:  A rectangle with length 4 and width 2. A rectangle with length 6 and width 3.

Getting length to length and width to width ratio:

$\dfrac{L_1}{L_2} = \dfrac{4}{6} = \dfrac{2}{3}\\\\\dfrac{W_1}{W_2} = \dfrac{2}{3} \\\\\\Thus, \dfrac{L_1}{L_2} = \dfrac{W_1}{W_2}$

Pair given are dilated version of each other.

• Case 3:  A rectangle with length 4 and width 3. A rectangle with length 3 and width 2.

Getting length to length and width to width ratio:

$\dfrac{L_1}{L_2} = \dfrac{4}{3}\\\\\dfrac{W_1}{W_2} = \dfrac{3}{2} \\\\\\Thus, \dfrac{L_1}{L_2} \neq \dfrac{W_1}{W_2}$

Pair given are not dilated version of each other.

• Case 4:  A rectangle with length 4 and width 3. A rectangle with length 2 and width 1.5.

Getting length to length and width to width ratio:

$\dfrac{L_1}{L_2} = \dfrac{4}{2} = \dfrac{2}{1}\\\\\dfrac{W_1}{W_2} = \dfrac{3}{1.5} = \dfrac{2}{1}\\\\\\Thus, \dfrac{L_1}{L_2} = \dfrac{W_1}{W_2}$

Pair given are dilated version of each other.

Thus, the pair of rectangle that will prove Carly's statement incorrect is: Option 3: A rectangle with length 4 and width 3. A rectangle with length 3 and width 2.

Learn more about dilation here:

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