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
