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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:
u^(2)^(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: $u^{2}{ }^{2}$

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Area and perimeter: 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:

u^{2}{ }^{2}

Understand the problem: Understand the problem. $\newline$ We are given the area of a square and asked to find the new area after the square is dilated by a scale factor of $2$ . The area of a square is given by the formula $A = s^2$ , where $s$ is the length of a side of the square. When a square is dilated by a scale factor, the lengths of the sides are multiplied by that factor. To find the new area, we will need to square the scale factor and multiply it by the original area.
Calculate new side length: Calculate the new side length after dilation. $\newline$ Since the area of the original square is $134 \text{ units}^2$ , we can find the original side length by taking the square root of the area. However, we do not need to calculate the original side length because we can directly use the scale factor to find the new area. The new area will be the original area multiplied by the square of the scale factor.
Calculate new area: Calculate the new area after dilation. $\newline$ The scale factor is $2$ , so we square it to get $2^2 = 4$ . We then multiply the original area by this value to get the new area. $\newline$ New Area = Original Area $\times$ (Scale Factor) $^2$ $\newline$ New Area = $134$ units $^2 \times 4$ $\newline$ New Area = $536$ units$^\(2\)

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