Geometry

grkmurthy · Senior Consultant Joined: 14 Oct 2007 Posts: 37

A square counter top has a square inlay of white tiles in the center surrounded by a strip of blue tiles of uniform width. The area of the white tiled portion and the area of blue tiled portion are in the ratio of 25 to 56. Which of the following could be the width of blue tiled strip?

I. 2
II. 3
III. 4

(1) I only.
(2) I & II only.
(3) I, II & III
(4) II & III only
(5) I & III only.

ksvickram · Senior Consultant Joined: 02 Jan 2008 Posts: 29

Area of the square / Area of BIG SQ - Area of small SQ = 25 / 56

a * a / {(a+2d) ^2} - {a * a} = 25 / 56

Comparing the Nrs, we can get that the area of smaller SQ = 25 ==> Side a = 5

Comparing the DRs, we get that 4 d ^2 + 4ad = 56 ==> d (a+d) = 14
Substituting a = 5 and 'd ' values from solution, only d = 2 satisfies this.