Question

charmaine has a patio that is in the shape of a rectangle with an area of 1200 ft². she 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 60 ft and a width of 20 ft. she plans on making the new length 2 times the current length and the new width 4 times the current width. (a) fill in the blanks to describe the size of charmaines new patio. new length × new width = new area □ ft × □ ft = □ ft² (b) how will the expansion change the area of the patio? the area of the new patio will be □ times the area of the current patio. (c) charmaines friend michael also wants to expand his rectangular patio. michael wants his new patio to be a rectangle that has 28 times the area of his current patio. he goes to charmaine for advice. fill in the blank so that charmaines advice to michael is correct. make the new length □ times the current length, and make the new width 4 times the current width.

Explanation:

Step1: Calculate new length

The current length is 60 ft and the new length is 2 times the current length. So, new length = $2\times60 = 120$ ft.

Step2: Calculate new width

The current width is 20 ft and the new width is 4 times the current width. So, new width = $4\times20=80$ ft.

Step3: Calculate new area

The area of a rectangle is length times width. So new area = new length $\times$ new width = $120\times80 = 9600$ ft².

Step4: Find ratio of new - to - old area

The old area is 1200 ft² and the new area is 9600 ft². The ratio is $\frac{9600}{1200}=8$.

Step5: Solve for Michael's length multiplier

Let the multiplier for the length be $x$. The multiplier for the width is 4 and the new area is 28 times the old area. Since area of rectangle = length $\times$ width, we have $x\times4 = 28$, so $x=\frac{28}{4}=7$.

Answer:

(a) 120 ft $\times$ 80 ft = 9600 ft²
(b) 8
(c) 7