Question

a rectangle is formed by placing two identical squares side by side. The area of the rectangle is 32 cm square. what is the perimeter of one square

Answer 1

Let's denote the side length of one square as \( s \).

When two identical squares are placed side by side, the rectangle formed has a length of \( 2s \) (since there are two sides of the square) and a width of \( s \).

The area of the rectangle can be computed as:
\[
\text{Area} = \text{length} \times \text{width} = 2s \times s = 2s^2
\]

Given that the area of the rectangle is 32 cm², we can set up the equation:
\[
2s^2 = 32
\]

Now, we will solve for \( s^2 \):
\[
s^2 = \frac{32}{2} = 16
\]

Taking the square root of both sides gives:
\[
s = \sqrt{16} = 4 \text{ cm}
\]

Now, to find the perimeter of one square, we use the formula for the perimeter of a square:
\[
\text{Perimeter} = 4s
\]
Substituting \( s = 4 \) cm:
\[
\text{Perimeter} = 4 \times 4 = 16 \text{ cm}
\]

Therefore, the perimeter of one square is \( \boxed{16 \text{ cm}} \).