Rectangular tiles, which measure 6 by 4 , are arranged without overlapping, to create a square. The minimum number of these tiles needed to make a square is
(A) 8
(B) 24
(C) 4
(D) 12
(E) 6
Rectangular tiles, which measure 6 by 4 , are arranged without overlapping, to create a square. The minimum number of these tiles needed to make a square is
(A) 8
(B) 24
(C) 4
(D) 12
(E) 6

## Solution

Since the rectangles measure $6 \times 4$ this means that the lengths of their sides are in a ratio of 3:2. This implies that we need two rectangles that have 6 as their side length to form one side of the square and for each of these rectangles we need three others to form the other side length. In total, we need $2 \times 3$ or 6 rectangles.

![](https://cdn.mathpix.com/cropped/2024_04_20_748fdafcde2a47412608g-405.jpg?height=428&width=437&top_left_y=1973&top_left_x=1386)

ANswer: (E)