Miranda enlarged a picture twice as shown below, each time using a scale factor of 3. A rectangle with length 6 inches and width 4 inches is enlarged twice. Which statements apply to the enlargements? Select three options. The area of the first enlargement is 72 square inches. The area of the second enlargement is 1,944 square inches. The area of the second enlargement is (3 squared) squared times the original area. The area of the second enlargement is 3 times the area of the first enlargement. The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor.
Question
Miranda enlarged a picture twice as shown below, each time using a scale factor of 3.
A rectangle with length 6 inches and width 4 inches is enlarged twice.
Which statements apply to the enlargements? Select three options. The area of the first enlargement is 72 square inches. The area of the second enlargement is 1,944 square inches. The area of the second enlargement is (3 squared) squared times the original area. The area of the second enlargement is 3 times the area of the first enlargement. The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor.
Solution
The statements that apply to the enlargements are:
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The area of the first enlargement is 72 square inches. This is because the scale factor is 3, so you multiply the length and the width of the original rectangle by 3. The original area is 6 inches * 4 inches = 24 square inches. When you enlarge it by a scale factor of 3, the area becomes 24 square inches * 3 * 3 = 72 square inches.
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The area of the second enlargement is 1,944 square inches. This is because the scale factor is 3, so you multiply the length and the width of the first enlargement by 3. The area of the first enlargement is 72 square inches. When you enlarge it by a scale factor of 3, the area becomes 72 square inches * 3 * 3 = 648 square inches. Then, you enlarge it again by a scale factor of 3, the area becomes 648 square inches * 3 * 3 = 1,944 square inches.
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The area of the second enlargement is (3 squared) squared times the original area. This is because the scale factor is 3, and the picture is enlarged twice. So, the total scale factor for the area is (3 * 3) * (3 * 3) = 81. The original area is 24 square inches, so the area of the second enlargement is 24 square inches * 81 = 1,944 square inches.
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