The floor of a rectangular room is covered with square tiles. The room is 10 tiles long and 5 tiles wide. The number of tiles that touch the walls of the room is
(A) 26
(B) 30
(C) 34
(D) 46
(E) 50
The floor of a rectangular room is covered with square tiles. The room is 10 tiles long and 5 tiles wide. The number of tiles that touch the walls of the room is
(A) 26
(B) 30
(C) 34
(D) 46
(E) 50

## Solution

If we draw a grid that is $10 \times 5$, it is easy to count the number of tiles that touch the walls. From the diagram we can see that there are 26 tiles that touch the walls. Notice that if the question had said a length of $l$ units ( $l$ an integer) and a width of $w$ units ( $w$ an integer) we would arrive at the formula: $2 w+2 l-4$ where 4 represents the 4 corner tiles which

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-441.jpg?height=277&width=526&top_left_y=233&top_left_x=1363)
would have been double counted. In this question, it would just be, $20+10-4=26$.

ANSWER: (A)