5 of 55 of 5 Items Question You want to divide a square piece of paper into two equivalent triangles. If the square measures 20 cm on each side, what will the third side of each triangle measure? (1 point) Responses 8.9 cm 8.9 cm 20 cm 20 cm 28.3 cm 28.3 cm 40 cm

Answer 1

To divide a square piece of paper into two equivalent triangles, we would typically cut it along one of its diagonals. Let's break down the solution:

1. The square has equal sides of 20 cm.
2. Dividing the square along the diagonal will result in two right-angled triangles.
3. Each triangle will have two sides that are each 20 cm (the sides of the square), and the third side is the hypotenuse of these right-angled triangles.

To find the length of the hypotenuse, we use the Pythagorean theorem, which is stated as:
\[ c = \sqrt{a^2 + b^2} \]
where \(a\) and \(b\) are the legs of the right triangle, and \(c\) is the hypotenuse.

Here, \(a = 20 \, \text{cm}\) and \(b = 20 \, \text{cm}\), so:
\[ c = \sqrt{20^2 + 20^2} \]
\[ c = \sqrt{400 + 400} \]
\[ c = \sqrt{800} \]
\[ c = \sqrt{16 \times 50} \]
\[ c = 4 \times \sqrt{50} \]
\[ c = 4 \times 7.07 \] (approximately, since \(\sqrt{50} \approx 7.07\))
\[ c \approx 28.3 \, \text{cm} \]

So, the third side of each triangle (the hypotenuse) will measure approximately 28.3 cm.

Therefore, the correct answer is **28.3 cm**.