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A square with an area of 21 units
^(2) is dilated by a scale factor of
(4)/(3). 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 $21$ units $^{2}$ is dilated by a scale factor of $\frac{4}{3}$ . 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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Dilations and parallel lines

Full solution

Q. A square with an area of

21

units

^{2}

is dilated by a scale factor of

\frac{4}{3}

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

\newline

Answer: units

^{2}

Find Side Length: First, we need to find the side length of the original square. Since the area of a square is equal to the side length squared, we can find the side length by taking the square root of the area. $\newline$ Area of original square = $21 \text{ units}^2$ $\newline$ Side length of original square = $\sqrt{21}$
Apply Scale Factor: Next, we apply the dilation scale factor to the side length of the original square to find the new side length. $\newline$ Scale factor = $\frac{4}{3}$ $\newline$ New side length = Original side length $\times$ Scale factor $\newline$ New side length = $\sqrt{21} \times \left(\frac{4}{3}\right)$
Calculate New Area: Now, we calculate the area of the new square using the new side length. The area of a square is the side length squared. $\newline$ Area of new square = $(\text{New side length})^2$ $\newline$ Area of new square = $(\sqrt{21} \times (\frac{4}{3}))^2$
Simplify Expression: We simplify the expression for the area of the new square by squaring both the square root of $21$ and the scale factor $(4/3)$ . $\newline$ Area of new square = $(21 \times (4/3)^2)$ $\newline$ Area of new square = $21 \times (16/9)$
Final Area Calculation: Finally, we multiply $21$ by $16/9$ to find the area of the new square. $\newline$ Area of new square = $21 \times (16/9)$ $\newline$ Area of new square = $21 \times 16 / 9$ $\newline$ Area of new square = $336 / 9$ $\newline$ Area of new square $\approx 37.3$ units $^2$ (rounded to the nearest tenth)

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