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jimmyjamesdonkey
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The perimeter of the square region S and the rectangular 30 Dec 2007, 11:19
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The perimeter of the square region S and the rectangular region R are equal. If the sides of R are in the ratio 2:3, what is the ratio of the area of the region R to the area of region S?

25:16

24:25

5:6

4:5

4:9

SOLVE!



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marcodonzelli
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The perimeter of the square region S and the rectangular 30 Dec 2007, 11:37
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jimmyjamesdonkey
The perimeter of the square region S and the rectangular region R are equal. If the sides of R are in the ratio 2:3, what is the ratio of the area of the region R to the area of region S?

25:16

24:25

5:6

4:5

4:9

SOLVE!
Show more


4s equals 2l+2w.....l equals 2/3*w and the area of R is 2/3 *w^2
s equals l/2 + w/2, substituting we have 5/6 *w and s^2 equals 25/36 *w^2...so 2/3 * 36/25 equals 24/25....B
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jimmyjamesdonkey
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The perimeter of the square region S and the rectangular 30 Dec 2007, 13:49
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Can you break down these equations you used easier to read. I solved this by using a plug-in #s method, but tried with formulas. Having trouble following your formula after 4s = 2l + 2w.
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The perimeter of the square region S and the rectangular 30 Dec 2007, 16:41
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24/25 for me as well

4S=2l+2w

2S=l+w and l=2/3w (from given ratio)

solve for s=5/6w

Ratio asked for is given by l*w / s^2

plug in all known numbers and you get 2/3*w^2 / 25/36*w^2

simplify to get B. Hope that halped.
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The perimeter of the square region S and the rectangular 30 Dec 2007, 21:29
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Simple method: we know the ratio of the sides of the rectangle are 2:3 so simply make the sides 2:3

Rectangle: 2x3 so perimeters is 2(2)+3(2) = 10 and area = 6
Square: same perimeter so 10/4 = 2.5 for each side. area equals 5/2*5/2 = 25/4

ratio of rectangle to square 6:25/4 (multiply each side by 4) 24:25

Answer B in ~30 seconds using mental math alone!
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The perimeter of the square region S and the rectangular 02 Jan 2008, 16:15
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jimmyjamesdonkey
The perimeter of the square region S and the rectangular region R are equal. If the sides of R are in the ratio 2:3, what is the ratio of the area of the region R to the area of region S?

25:16

24:25

5:6

4:5

4:9

SOLVE!
Show more

This problem was much easier to do once I got off my fat ass and did it on a piece of paper rather than in my head =)

anyway:

Lets say we have S as the side of square S.

4S=2l+2w

2l=3w --> l=1.5w

4S=2(1.5w)+2w --> 4S=5W --> S=5W/4

Now we want to know lw/s^2 --> s^2=25w^2/16

also plug in l on top

1.5w*w/25w^2/16---> 3/2*16/25 --> 48/50---> 24/25

B



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Hi there,
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Thank you for understanding, and happy exploring!