A ratio question from conept series

GRE Quant Problem Solving
1

Hi, I was not sure how I can judge the ratio below is the same as 3/4.

It’s from Linear and Quadratic Equations Practice.

A rectangular rug covers half of a rectangular floor that is 9 feet wide and 12 feet long. If the dimensions of the rug are in the same ratio as those of the floor, how many feet long is the rug?
(A) 6
(B) 21/2
(C) 2√7
(D) 6√2
(E) 4√6

In the class, there were back solving methods.

For (B), the ratio is 10.5: 5.14, and how can I know the exact ratio?

For (D), the ratio is 8.4:5.14, and it’s the answer. but how can I know it’s 3:4?
when I divided 5.14/8.4, the result is 0.7642… and 3/4 is 0.33333…

2

Area of rug = xy=54

For option B we get 10.5 : 5.14
We can see here that 5.14 * 2 gives us 10.28.
So we can say that this ration is more like a 2 : 1 ratio

For option D we get 8.485 : 6.364
Getting rid of the decimals, we can say that this is approximately 8 : 6 and dividing by 2 on both sides, we get 4 : 3

3

Thank you very much. so we can just judge by approximate numbers right? I thought there could be a way to have exact ratio.

4

Yea totally, approximations works most of the times.