An equilateral triangle of side 16cm has the same perimeter as a square. Find the of the square please explain well

Answer 1

When an equilateral triangle and a square have the same perimeter, the first step is to calculate the perimeter of the equilateral triangle.

An equilateral triangle has three equal sides. Given that each side of the triangle is 16 cm, the perimeter \(P_{triangle}\) of the equilateral triangle is calculated as follows:
\[
P_{triangle} = 3 \times \text{side length of the triangle} = 3 \times 16 \text{ cm} = 48 \text{ cm}
\]

Since the triangle's perimeter equals the square's perimeter, the perimeter of the square \(P_{square}\) is also 48 cm. A square has four equal sides, so we can calculate the length of one side of the square \(s\) by dividing the perimeter by 4:
\[
s = \frac{P_{square}}{4} = \frac{48 \text{ cm}}{4} = 12 \text{ cm}
\]

Therefore, the side length of the square is 12 cm.