A rectangular floor is fully covered with square tiles of identical size.The tiles on the edge are white and t

Question

A rectangular floor is fully covered with square tiles of identical size.The tiles on the edge are white and the tiles in the interior are red. the number of white tiles is the same as the number of red tiles. a possible value of the number of tiles along one edge of the floor is
(a) 10
(b) 12
(c) 14
(d) 16

Answer 1

Hi Rohit C

Only (b) is a possible answer.

Lets say you construct the floor with an outer rectangle of side lengths x and (y+2). The number of white squares will by equal to

x + (y+2) + x + (y+2) - 4 (because the four corner squares were counted twice)
= 2x + 2y

The number of red squares will be given by

(x-2)*y
= yx - 2y

Now we want the numbers of red and white squares to be equal, so:

2x + 2y = yx - 2y
2x - xy + 4y = 0.

Now you've been given four possible values for x: 10, 12, 14, 16. Substitute each into the equation above and see which returns an integer result for y. Only (b) x=12 does. For x=12, y=3 and there are 30 red and 30 white squares.


Hope this helps!
The Chicken

Answer 2

let x & y be the number of tiles on each side

white tiles = 2x + 2(y-2) - substract the overlapping corner tiles
red tiles = (x-2)(y-2) - substract 1 edge tile at each end

2x + 2(y-2) = (x-2)(y-2)
2x + 2y - 4 = xy -2x - 2y + 4
4x - xy = 8 - 4y = 4(2 - y)
x = 4(2-y)/(4-y)

if y = 10, x = -32/-6
if y = 12, x = -40/-8 = 5
if y = 14, x = -48/-10
if y = 16, x = -56/-12

Therefore, answer is (b) because only this will result in integer x.

Answer 3

well im not sure but id have to say C considering it is a rectangular and so all the sides are unequal and if u divide 14 by 2 its 7 which isnt a even number all the others divided by 2 are even

Answer 4

b is the answer

30 on the outside 30 on the inside

the power of a picture and trial and error :)

Answer 5

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