nave81 wrote:

In the diagram above, the fourteen rectangular tiles are all identical. What percent of the area of rectangle ABCD is covered by the tiles?

(1) ABCD is a square.

(2) EFGH is a square.

Figure attached

Suppose the dimention of the tiles are l*b

STAT1

Let side of Square ABCD = a

then if you consider side AB then

AB = a = 3l + 2b

if you consider side AD then

AD = a = 4l

so, 4l = 3l + 2b

or, l =2b

Also, we know that a = 4l

so, l = a/4

b = l/2 = a/8

So, we can find the area of the tile in terms of "a"

Area of all the tiles = (constant)* a^2

So, we can find the percentage of area occupied by tile = ((constant)* a^2 / a^2 ) * 100

So, SUFFICIENT

STAT2

Let side of EFGH = c

then if you consider EF then

EF = c = 3l

if you consider EH then

EH = c = 2l + l-b + l-b = 4l-2b

=> 3l = 4l-2b

l = 2b

And we have c = 3l

=> l = c/3

b = l/2 = c/6

AB = 4l = 4c/3

So, we can find area of ABCD in terms of C And we can find area of the tiles in terms of c

So, we can find the percentage of area occupied by tiles

So, SUFFICIENT

Hence answer will be D

Hope it helps!

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