To solve this problem, let’s break down the information given:

1. Five identical squares are joined to form a rectangle.
2. Area of the rectangle = 245 cm².

Let $s$ be the side length of each square. Then, the area of each square is $s^2$, and since there are five squares, the combined area is $5s^2$.

Since these five squares form a rectangle, the area of the rectangle (245 cm²) is equal to $5s^2$. Therefore: $5s^2 = 245$ $s^2 = \frac{245}{5} = 49$ $s = \sqrt{49} = 7 \, \text{cm}$

Now, the five squares could be arranged in either a row (1x5) or in two rows and two columns (2x5 arrangement).

• If arranged in a row: The rectangle’s dimensions would be $7$ cm (height) and $5 \times 7 = 35$ cm (length).
• If arranged in two rows: The dimensions would be $2 \times 7 = 14$ cm (height) and $\frac{5}{2} \times 7 = 35$ cm (length).

The perimeter $P$ of a rectangle is calculated by: $P = 2 \times (\text{length} + \text{height}) = 2 \times (35 + 7) = 2 \times 42 = 84 \, \text{cm}$

So, the perimeter of the rectangle is 84 cm (option B).

Would you like further details, or do you have any questions?

1. How do we determine the arrangement of the squares?
2. Could the perimeter change if arranged differently?
3. Why is the side length calculated using square roots?
4. How does the arrangement affect the rectangle's dimensions?
5. What would the perimeter be if only four squares were used?

Tip: Always recheck your dimensions after calculating to ensure they match the given area.