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A square with an area of 6 units ^(2) is dilated by a scale factor of (2)/(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 66 units 2 ^{2} is dilated by a scale factor of 23 \frac{2}{3} . Find the area of the square after dilation. Round your answer to the nearest tenth, if necessary.\newlineAnswer: units 2 ^{2}

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Full solution

Q. A square with an area of 66 units 2 ^{2} is dilated by a scale factor of 23 \frac{2}{3} . Find the area of the square after dilation. Round your answer to the nearest tenth, if necessary.\newlineAnswer: units 2 ^{2}
  1. Find Side Length: Determine 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. Area=side length2\text{Area} = \text{side length}^2 6=side length26 = \text{side length}^2 side length=6\text{side length} = \sqrt{6}
  2. Calculate New Side Length: Calculate the side length of the square after dilation.\newlineThe new side length is found by multiplying the original side length by the scale factor.\newlineNew side length = original side length ×\times scale factor\newlineNew side length = 6×(23)\sqrt{6} \times \left(\frac{2}{3}\right)
  3. Calculate New Area: Calculate the area of the square after dilation.\newlineThe area of the dilated square is equal to the new side length squared.\newlineNew area = (new side length)2(\text{new side length})^2\newlineNew area = (6×(23))2(\sqrt{6} \times (\frac{2}{3}))^2\newlineNew area = 6×(23)26 \times (\frac{2}{3})^2\newlineNew area = 6×(49)6 \times (\frac{4}{9})\newlineNew area = 249\frac{24}{9}\newlineNew area = 2.666...2.666...\newlineSince we need to round to the nearest tenth, the new area is approximately 2.72.7 units2^2.

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