KN/MN

[sharath.nair]

In the figure, what is the ratio of KN/MN?

(1) The perimeter of rectangle KLMN is 30 cm.

(2) The three small rectangles have the same dimensions.

I selected choice E.

OA is C.

Could you please post the solution?

Thanks!

[venkat_yj]

(2) by itself gives the ratio of KN/MN. Not sure if C is the right answer.

Here is the sol:

Since the three rectangles have same dimensions, say width=x, length =y

KN=y=2x
MN=y+x

KN/MN = 2x/3x = 2/3

[banakida]

I agree with venkat_yj that it looks like B is the correct answer. Are you sure about C?

[RonPurewal]

yeah, look again. should be (b); the second statement alone is sufficient.

look at the MIDDLE HORIZONTAL LINE in the diagram, where the 2 vertically oriented rectangles meet the horizontally oriented one.
if "x" is the shorter dimension (i'm going to avoid using the words "length" and "width" because of the sideways flipped rectangles), then, looking at that meeting point, we can see that the longer dimension is "2x".

thus the given ratio is 2x / (2x + x), or 2:3.
sufficient.

you could also try inputting particular dimensions that satisfy statement (2), and noting that all of them yield a final ratio of 2:3.

[rx_11]

Hi, Ron,

I am stucked with this question. The OA is B and almost all people have said that the answer is definitely B. However, I just can't get it. I still think that from the information of (2), we cannnot know the ratio of KN/MN.

To prove my point, I draw a counterexample.

L_______________M
|--------|--------|
|--------|--------| 2
|_______|___3___|
|-----------------| 1
|_______________|
K--------6--------N


In this figure above, the dimension of the three rectangles are the same, but KN/MN = 2/1, not 2/3. Could u explain this? How do you know KN=2x from your explanation above?

[dmitryknowsbest]

Hi rx_11,

The problem with your counterexample is that your rectangles do not all have the same dimensions. The top rectangles are 3x2 and the bottom rectangle is 6x1. If you make them all 3x2, you will get a large rectangle with a width of 6 and a height of 9, for a ratio of 2/3.

[rx_11]

Hi rx_11,

The problem with your counterexample is that your rectangles do not all have the same dimensions. The top rectangles are 3x2 and the bottom rectangle is 6x1. If you make them all 3x2, you will get a large rectangle with a width of 6 and a height of 9, for a ratio of 2/3.

Hi, dmitry,

Do you mean that the "dimension" is not necessarily equal to "area"? Could you tell me what is "dimension"? I used to think that the "dimension" is equal to "area"..

[jnelson0612]

Hi rx_11,

The problem with your counterexample is that your rectangles do not all have the same dimensions. The top rectangles are 3x2 and the bottom rectangle is 6x1. If you make them all 3x2, you will get a large rectangle with a width of 6 and a height of 9, for a ratio of 2/3.

Hi, dmitry,

Do you mean that the "dimension" is not necessarily equal to "area"? Could you tell me what is "dimension"? I used to think that the "dimension" is equal to "area"..

Hi rx_11,
Yes, the term "dimensions" is not referring to area. The term "dimensions" refers to the lengths and widths of these three rectangles. In your example you used two rectangles with the same lengths and widths but a third with a different length and width, even though the areas of all three triangles were the same. If you use the same lengths and widths for all three triangles you can solve this problem using statement 2.

[rachelhong2012]

When I looked at the bigger figure, I see three smaller rectangles coming together to form the bigger rectangles.

If we're talking in terms of the smaller rectangle, then then longer line is the length and the shorter line is the width. Let's call these smaller rectangles A, B and C The two on the top being A and B from left to right, and the one on the bottom being C

ratio KN/MN?

(length of smaller rectangle C)/ (length of smaller rectangle B + width of smaller rectangle C)

Hope you see that statement 1 is clearly insufficent because knowing perimeter doesn't help us determine the exact dimension of lengths and widths.

Statement 2 is sufficient because:

All three rectangles have the same dimensions,

in other words, combine this with my equation, I now know that:

(length of smaller rectangle C)/ (length of smaller rectangle B + width of smaller rectangle C)

is the same as
(length of smaller rectangle C)/ (length of smaller rectangle c + width of smaller rectangle C)

IF you rewrite the equation, it becomes:

length/length + length/width = ?
1 + length/width = ?
The real question disguised is what is the proportion between the length and width of the smaller rectangle?

Look at line segments LM and KN and you will see that the length is made up of two widths, so we know their proportion.

Sufficient.

[jnelson0612]

Thanks rachel, and everyone!