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Joe has a patio that is in the shape of a rectangle with an area of 600ft2. He has decided to expand the patio so that it can hold more furniture. The new patio will be a larger rectangle. The current patio has a length of 30ft and a width of 20ft. He plans on making the new length 4 times the current length and the new width 5 times the current width.(a)Fill in the blanks to describe the size of Joe's new patio.New lengthft×New widthft=New areaft2(b)How will the expansion change the area of the patio?Theareaofthenewpatiowillbetimestheareaofthecurrentpatio.(c)Joe's friend Greg also wants to expand his rectangular patio. Greg wants his new patio to be a rectangle that has 15 times the area of his current patio. He goes to Joe for advice. Fill in the blank so that Joe's advice to Greg is correct.Makethenewlengthtimesthecurrentlength,andmakethenewwidth3timesthecurrentwidth.

Question

Joe has a patio that is in the shape of a rectangle with an area of 600ft2. He has decided to expand the patio so that it can hold more furniture. The new patio will be a larger rectangle. The current patio has a length of 30ft and a width of 20ft. He plans on making the new length 4 times the current length and the new width 5 times the current width.(a)Fill in the blanks to describe the size of Joe's new patio.New lengthft×New widthft=New areaft2(b)How will the expansion change the area of the patio?Theareaofthenewpatiowillbetimestheareaofthecurrentpatio.(c)Joe's friend Greg also wants to expand his rectangular patio. Greg wants his new patio to be a rectangle that has 15 times the area of his current patio. He goes to Joe for advice. Fill in the blank so that Joe's advice to Greg is correct.Makethenewlengthtimesthecurrentlength,andmakethenewwidth3timesthecurrentwidth.

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Solution

(a) The new length of Joe's patio will be 4 times the current length, so the new length will be 430 = 120ft. The new width will be 5 times the current width, so the new width will be 520 = 100ft. Therefore, the new area of the patio will be 120ft * 100ft = 12,000ft2.

So, the blanks should be filled as follows: New length: 120ft New width: 100ft New area: 12,000ft2

(b) The area of the new patio will be 12,000ft2, and the area of the current patio is 600ft2. Therefore, the area of the new patio will be 12,000/600 = 20 times the area of the current patio.

So, the blank should be filled as follows: The area of the new patio will be 20 times the area of the current patio.

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

So, the blanks should be filled as follows: Make the new length 5 times the current length, and make the new width 3 times the current width.

This problem has been solved

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