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Tammy's vegetable garden has an area of 200ft2. It is the shape of a rectangle with a length of 20ft and a width of 10ft. She has decided to expand the garden to make room for several new varieties of lettuce. The new garden will be a larger rectangle. She plans on making the new length 3 times the current length and the new width 3 times the current width.(a)Fill in the blanks to describe the size of Tammy's new garden.New lengthft×New widthft=New areaft2(b)How will the expansion change the area of the garden?Theareaofthenewgardenwillbetimestheareaofthecurrentgarden.(c)Tammy's friend Ivan also wants to expand his rectangular garden. Ivan wants his new garden to be a rectangle that has 15 times the area of his current garden. He goes to Tammy for advice. Fill in the blank so that Tammy's advice to Ivan is correct.Makethenewlength5timesthecurrentlength,andmakethenewwidthtimesthecurrentwidth.

Question

Tammy's vegetable garden has an area of 200ft2. It is the shape of a rectangle with a length of 20ft and a width of 10ft. She has decided to expand the garden to make room for several new varieties of lettuce. The new garden will be a larger rectangle. She plans on making the new length 3 times the current length and the new width 3 times the current width.(a)Fill in the blanks to describe the size of Tammy's new garden.New lengthft×New widthft=New areaft2(b)How will the expansion change the area of the garden?Theareaofthenewgardenwillbetimestheareaofthecurrentgarden.(c)Tammy's friend Ivan also wants to expand his rectangular garden. Ivan wants his new garden to be a rectangle that has 15 times the area of his current garden. He goes to Tammy for advice. Fill in the blank so that Tammy's advice to Ivan is correct.Makethenewlength5timesthecurrentlength,andmakethenewwidthtimesthecurrentwidth.

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Solution

(a) The new length of Tammy's garden will be 3 times the current length, so the new length will be 3 * 20ft = 60ft. The new width will be 3 times the current width, so the new width will be 3 * 10ft = 30ft. Therefore, the new area of the garden will be the new length times the new width, which is 60ft * 30ft = 1800ft2.

So, the size of Tammy's new garden is: New length: 60ft New width: 30ft New area: 1800ft2

(b) The area of the new garden will be 1800ft2, and the area of the current garden is 200ft2. Therefore, the new garden's area is 1800ft2 / 200ft2 = 9 times the area of the current garden.

(c) If Ivan wants his new garden to be a rectangle that has 15 times the area of his current garden, he should make the new length 5 times the current length, and make the new width 3 times the current width. This is because 5 * 3 = 15, which will make the new area 15 times the current area.

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