Rectangled

sampath wrote:The sides of a rectangle are all produced in order, in such a way that the length of each side is increased by k times itself. The area of the new quadrilateral formed becomes 2.5 times the area of the original rectangle.

The value of k is:
(A) 1/3 (B) 1/4 (C) 1/2 (D) 2/3 (E) 1/5

Let the original rectangle have length L and width W.
So, the area of the original rectangle is LW

After the increase, the length of the new rectangle is kL and new width is kW.
So, the area of the original triangle is (kL)(kW) = (k^2)(LW)

We are told that the area of the new rectangle is 2.5 times the area of the original rectangle.

So, we can say that (k^2)(LW) / (LW) = 2.5
When we simplify, we get k^2 = 2.5
Since the answers are given as fractions, we can rewrite 2.5 as 5/2 to get k^2 = 5/2
To solve for k, we'll take the square root of both sides to get k = root5/root2

This does not appear to be one of the answer choices, but it should be.

Cheers,
Brent

rppala90 wrote:"length of each side is increased by k times itself"

If old length is "L" then what will be the new length ?
L + KL = (k+1)L
or
KL ?

Either way the options given does not seem to be correct.

Yes, I struggled with that portion of the question as well.
As you correctly mentioned, rppala90, even if it does mean L + kL, the answer choices are still incorrect.

There's also some strangeness around the wording of "the sides of a rectangle are all produced in order."

In order?

Given the ambiguity of this question, I'd have to assume that this is not an official GMAT question.

What's the source, sampath?

Cheers.
Brent

I should also point out the error in my initial solution.

If the length of a side is increased by some value, I should have said that the new length is L plus something, not L times something. My bad.

That said, I'm going to hide my error behind the ambiguity of the question and the fact that the answer choices do not seem to work no matter how you look at it

Cheers,
Brent

GmatKiss wrote:suppose the old area l*b=>10
New area is increased 2.5 times, new area=> 25

Means, l.k*b=25 (Length should have increase by 2.5 times) b is constant.
so K should be 2.5

Possibly, but even with that interpretation, the answer choices don't match up.

Cheers,
Brent