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The problem provides the area of a rectangle, which is \( 15 \, \text{cm}^2 \). The rectangle's height is given as \( 5 \, \text{cm} \), and the width is described as \( q - 2 \, \text{cm} \), where \( q \) is what we are solving for.

The area \( A \) of a rectangle is calculated by multiplying the width by the height:
\[
A = \text{width} \times \text{height}
\]

Substitute the known values into this formula:
\[
15 = (q - 2) \times 5
\]

Now, solve for \( q \):

1. Divide both sides by 5:
\[
\frac{15}{5} = q - 2
\]
\[
3 = q - 2
\]

2. Add 2 to both sides:
\[
q = 3 + 2 = 5
\]

Thus, \( q = 5 \, \text{cm} \).

Would you like a deeper explanation or have any further questions? Here are some related questions:

1. How do you find the area of different geometric shapes?
2. What happens to the area if the width or height increases by 1 cm?
3. Can you solve for \( q \) if the area is doubled?
4. How can this concept apply to other polygons?
5. What is the difference between perimeter and area?

**Tip:** Always double-check the units when solving geometric problems to ensure consistency.

The area of the rectangle is 15 cm². What is q in centimetres (cm)?

Learn how to find the unknown side length of a rectangle with an area of 15 cm² using algebraic equations. This problem covers essential geometry and algebra concepts, including area calculations. Suitable for students in Grades 6-8.

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