In your experimentation, did you consider the case when all four sides of the rectangle are equal? That is, did you consider the case of a square? See what happens in this special case!

Question

Homi · Accepted Answer

Understand the Question

A square is a special type of rectangle where all four sides are equal in length.
If we set both the length and width of the rectangle equal to $s$ , we can observe how the standard perimeter and area formulas simplify for a square.

Step 1 · Sides of a Square as a Special Rectangle

For a rectangle with length $L$ and width $W$ , when all four sides are equal, it forms a square where both dimensions equal a common side length $s$ : Diagram 1

$L = s, \quad W = s$

Step 2 · Perimeter of the Square

Using the perimeter formula for a rectangle $2 \times (\text{length} + \text{width})$ :

\begin{aligned} \text{Perimeter} &= 2 \times (s + s) \\[0.6em] &= 2 \times (2s) \\[0.6em] &= 4s \end{aligned}

Step 3 · Area of the Square

Using the area formula for a rectangle $\text{length} \times \text{width}$ :

\begin{aligned} \text{Area} &= s \times s \\[0.6em] &= s^2 \end{aligned}

Answer

When a rectangle becomes a square of side $s$ , length and width are equal ( $L = W = s$ ). The Perimeter becomes $4s$ and the Area becomes $s^2$ .

Common Mistakes

Confusing Perimeter and Area: Adding sides gives the perimeter ( $4s$ ), while multiplying side by side gives the area ( $s^2$ ). Do not mix the two formulas.
Rectangle vs. Square Classification: Assuming a square is entirely different from a rectangle; every square is a rectangle with equal adjacent sides.

Question 9

More questions in A

Construct

2. Wavy Wave

Explore

Math Talk