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Sienna planned a rectangular pool, as shown in the scale drawing below. A rectangle with length 11 inches and width 7 inches. Sienna used the scale drawing above to create a pool that is 14 ft wide mc005-2.jpg 22 ft long. She then decided to make a pool with a final length of 33 ft. Which expression finds the change in scale factor for the longer pool Sienna is building? StartFraction 11 inches over 27.5 feet EndFraction StartFraction 22 feet over 11 inches EndFraction StartFraction 22 feet over 27.5 feet EndFraction StartFraction 27.5 feet over 22 feet EndFraction

Question

Sienna planned a rectangular pool, as shown in the scale drawing below.

A rectangle with length 11 inches and width 7 inches. Sienna used the scale drawing above to create a pool that is 14 ft wide mc005-2.jpg 22 ft long. She then decided to make a pool with a final length of 33 ft. Which expression finds the change in scale factor for the longer pool Sienna is building? StartFraction 11 inches over 27.5 feet EndFraction StartFraction 22 feet over 11 inches EndFraction StartFraction 22 feet over 27.5 feet EndFraction StartFraction 27.5 feet over 22 feet EndFraction

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Solution

The scale factor is the ratio of the lengths of corresponding sides in two similar geometric figures. In this case, we are looking for the change in scale factor from the original pool to the larger pool that Sienna is building.

The original pool has a length of 22 feet and a width of 14 feet. In the scale drawing, these dimensions are represented as 11 inches and 7 inches, respectively. Therefore, the scale factor of the original pool is 22 feet/11 inches = 2 feet/inch.

Sienna is planning to build a larger pool with a length of 33 feet. To find the change in scale factor, we need to compare the scale factor of the larger pool to the scale factor of the original pool.

The scale factor of the larger pool is 33 feet/11 inches = 3 feet/inch.

Therefore, the change in scale factor is 3 feet/inch - 2 feet/inch = 1 foot/inch.

So, the correct expression to find the change in scale factor for the longer pool Sienna is building is "StartFraction 33 feet over 11 inches EndFraction - StartFraction 22 feet over 11 inches EndFraction".

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