Given that the side length of the equilateral triangle is 16 cm, we need to determine the area of a square that has the same perimeter as this triangle.
First, we calculate the perimeter of the equilateral triangle:
\[
\text{Perimeter of the equilateral triangle} = 3 \times \text{side length} = 3 \times 16 \text{ cm} = 48 \text{ cm}
\]
The perimeter of the square is given to be equal to the perimeter of the equilateral triangle:
\[
\text{Perimeter of the square} = 48 \text{ cm}
\]
The perimeter of a square is \(4 \times \text{side length of the square}\). Let \( s \) be the side length of the square. Then:
\[
4s = 48 \text{ cm}
\]
Solving for \( s \), we divide both sides by 4:
\[
s = \frac{48}{4} \text{ cm} = 12 \text{ cm}
\]
Now, we calculate the area of the square, which is given by side length squared:
\[
\text{Area of the square} = s^2 = 12^2 = 144 \text{ cm}^2
\]
Thus, the area of the square is:
\[
\boxed{144 \text{ cm}^2}
\]
An equilateral triangle of side 16cm has the same perimeter as a square. Find the area of the square
1 answer