Question

A square tablecloth has an area of 4m². If the tablecloth is cut in half from corner to corner, how long is the cut?

A) 2 meters
B) 2√2 meters
C) 4 meters
D) 8 meters

Answer 1

The length of the cut when a 4m² square tablecloth is cut from corner to corner is found by calculating the diagonal using the Pythagorean theorem. The diagonal, in this case, is 2√2 meters, so the correct answer is B) 2√2 meters.

Step-by-step explanation:

To find the length of the cut when a square tablecloth with an area of 4m² is cut from corner to corner, we first need to determine the side length of the tablecloth. Since the area of a square is calculated by squaring the side length (side length × side length), we can take the square root of the area to find the side length. The square root of 4m² is 2m, meaning each side of the tablecloth is 2 meters long.

When you cut a square from corner to corner, you are cutting along the diagonal. The diagonal of a square can be found using the Pythagorean theorem (a² + b² = c²), where a and b are the sides of the square, and c is the diagonal. Applying this theorem to our square:

2m² + 2m² = c²

4m² + 4m² = c²

8m² = c²

To find c, we take the square root of 8m², which gives us:

c = √(8m²)

c = 2√2 meters

Therefore, the length of the cut is 2√2 meters, making the correct option B