In the diagram the five smaller rectangles are identical in size and shape. The ratio of $A B: B C$ is
(A) $3: 2$
(D) $5: 3$
(B) 2:1
(E) $4: 3$
(C) 5:2

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-140.jpg?height=215&width=263&top_left_y=478&top_left_x=1386)
In the diagram the five smaller rectangles are identical in size and shape. The ratio of $A B: B C$ is
(A) 3:2
(B) 2:1
(D) $5: 3$
(E) $4: 3$
(C) $5: 2$

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-234.jpg?height=249&width=314&top_left_y=244&top_left_x=1469)

## Solution

We let the width of each rectangle be $x$ units and the length of each rectangle be $3 x$ units. (We have illustrated this in the diagram.) The length, $A B$, is now $3 x+x+x$ or $5 x$ units and $B C=3 x$. Since $A B: B C=5 x: 3 x$

![](https://cdn.mathpix.com/cropped/2024_04_20_faa9db06d997f2a5b9b1g-234.jpg?height=244&width=330&top_left_y=580&top_left_x=1453)

$$
=5: 3, \quad x \neq 0
$$

ANSWER: (D)