A rectangle with an area of 140 units ^(2) is the image of a rectangle that was dilated by a scale factor of (3)/(4). Find the area of the preimage, the original rectangle, before its dilation. Round your answer to the nearest tenth, if necessary. Answer: units ^(2)

Understand problem and relationship: Understand the problem and the relationship between the area of the image and the preimage when dilation occurs. The area of the image after dilation is given as 140 square units. The scale factor of the dilation is 3/4, which means every linear dimension of the preimage is multiplied by 3/4 to get the image. The area of the preimage can be found by dividing the area of the image by the square of the scale factor.Calculate preimage area: Calculate the area of the preimage using the scale factor. The area of the preimage (A_preimage) is equal to the area of the image (A_image) divided by the square of the scale factor (k^2). A_preimage = A_image / k^2 A_preimage = 140 / (3/4)^2Perform calculation: Perform the calculation. A_preimage = 140 / (9/16) To divide by a fraction, multiply by its reciprocal. A_preimage = 140 * (16/9) A_preimage = 140 * 16 / 9 A_preimage = 2240 / 9 A_preimage ≈ 248.9 (rounded to the nearest tenth)

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A rectangle with an area of 140 units
^(2) is the image of a rectangle that was dilated by a scale factor of
(3)/(4). Find the area of the preimage, the original rectangle, before its dilation. Round your answer to the nearest tenth, if necessary.
Answer: units
^(2)

A rectangle with an area of $140$ units $^{2}$ is the image of a rectangle that was dilated by a scale factor of $\frac{3}{4}$ . Find the area of the preimage, the original rectangle, before its dilation. Round your answer to the nearest tenth, if necessary. $\newline$ Answer: units $^{2}$

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Q. A rectangle with an area of

140

units

^{2}

is the image of a rectangle that was dilated by a scale factor of

\frac{3}{4}

. Find the area of the preimage, the original rectangle, before its dilation. Round your answer to the nearest tenth, if necessary.

\newline

Answer: units

^{2}

Understand problem and relationship: Understand the problem and the relationship between the area of the image and the preimage when dilation occurs. $\newline$ The area of the image after dilation is given as $140$ square units. The scale factor of the dilation is $\frac{3}{4}$ , which means every linear dimension of the preimage is multiplied by $\frac{3}{4}$ to get the image. The area of the preimage can be found by dividing the area of the image by the square of the scale factor.
Calculate preimage area: Calculate the area of the preimage using the scale factor. $\newline$ The area of the preimage $A_{\text{preimage}}$ is equal to the area of the image $A_{\text{image}}$ divided by the square of the scale factor $k^2$ . $\newline$ $A_{\text{preimage}} = \frac{A_{\text{image}}}{k^2}$ $\newline$ $A_{\text{preimage}} = \frac{140}{(\frac{3}{4})^2}$
Perform calculation: Perform the calculation. $\newline$ $A_{\text{preimage}} = \frac{140}{\left(\frac{9}{16}\right)}$ $\newline$ To divide by a fraction, multiply by its reciprocal. $\newline$ $A_{\text{preimage}} = 140 \times \left(\frac{16}{9}\right)$ $\newline$ $A_{\text{preimage}} = 140 \times \frac{16}{9}$ $\newline$ $A_{\text{preimage}} = \frac{2240}{9}$ $\newline$ $A_{\text{preimage}} \approx 248.9$ (rounded to the nearest tenth)