The perimeters of square region S and rectangular region R are equal. If the sides of R are in the ratio 2:3 , what is the ratio of the area of region R to the are of region S ?
A 25:16
B 24:25
C 5:6
D 4:5
E 4:9
Since a square has 4 equal sides, plug in multiples of 4.
Rectangle R:
Since L:W = 2:3, let L = 4*2 = 8 and W = 4*3 = 12.
Then:
Perimeter = L+W+L+W = 8+12+8+12 = 40.
Area = L*W = 8*12 = 96.
Square S:
Since S and R have the same perimeter, P = 40.
Since perimeter = 40, S=10.
Area = S² = 10² = 100.
Resulting ratio:
R/S = 96/100 = 48/50 = 24/25.
The correct answer is
B.
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