another question

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The perimeters of square region S and rectangular region R are equal. If sides of R are in the ratio 2:3, what is the ratio of the area of region R to the area of region S?

a)25:16
b)24:25
c)5:6
d)4:5
e)4:9

I don't understand the underlined part above, what are the values of the sides of R?
 
The ratio you have underlined means that the sides of the rectangle are

2 to 3. That is, the long sides will have 3 units length for every 2 units for

the other two sides. For simplicity, make a rectangle with side lengths 3

for the longer sides and length 2 for the shorter sides.

That way the perimeter will be 3+3+2+2=10. See?. That gives the

rectangle an area of (3)(2)=6=area R

Now, the square has the same perimeter, so it's sides would have to be

10/4=2.5. This gives the square an area of (2.5)(2.5)=6.25=25/4=area S.

Now, do you see the area ratio they want?. R/S.
 
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