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A square with an area of 134 units
^(2) is dilated by a scale factor of 2 . Find the area of the square after dilation. Round your answer to the nearest tenth, if necessary.
Answer: units
^(2)

A square with an area of $134$ units $^{2}$ is dilated by a scale factor of $2$ . Find the area of the square after dilation. Round your answer to the nearest tenth, if necessary. $\newline$ Answer: units $^{2}$

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Scale drawings: word problems

Full solution

Q. A square with an area of

134

units

^{2}

is dilated by a scale factor of

2

. Find the area of the square after dilation. Round your answer to the nearest tenth, if necessary.

\newline

Answer: units

^{2}

Understand Problem and Given: Understand the problem and what is given. $\newline$ We are given the area of a square and a scale factor by which the square is dilated. We need to find the new area after dilation.
Calculate Original Side Length: Calculate the side length of the original square. $\newline$ The area of a square is given by the formula $A = s^2$ , where $A$ is the area and $s$ is the side length. We need to find $s$ for the original square. $\newline$ Given $A = 134$ units $^2$ , we can write: $\newline$ $s^2 = 134$ $\newline$ $s = \sqrt{134}$
Apply Scale Factor: Apply the scale factor to the side length. $\newline$ The new side length after dilation will be twice the original side length because the scale factor is $2$ . $\newline$ New side length $s' = 2 \times s$ $\newline$ $s' = 2 \times \sqrt{134}$
Calculate New Area: Calculate the new area after dilation. $\newline$ The new area $A'$ will be the square of the new side length. $\newline$ $A' = (s')^2$ $\newline$ $A' = (2 \times \sqrt{134})^2$ $\newline$ $A' = 4 \times 134$ $\newline$ $A' = 536$ units $^2$

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