Final answer:
The diagonal distance in Sally's rectangular bedroom, which measures 4 meters by 4 meters, is approximately 5.7 meters when calculated using the Pythagorean theorem.
Step-by-step explanation:
To calculate the diagonal distance from one corner of Sally's room to the opposite corner, we can use the Pythagorean theorem. This theorem states in a right-angled triangle that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. Since Sally's room is rectangular and the length and width are both 4 meters, we can consider the diagonal as the hypotenuse of a right-angled triangle with both the other sides being 4 meters.
Step 1: Write the Pythagorean theorem:
c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
Step 2: Substitute the known values:
diagonal^2 = 4^2 + 4^2
Step 3: Calculate the square of the sides:
diagonal^2 = 16 + 16
Step 4: Add the values:
diagonal^2 = 32
Step 5: Find the square root to find the diagonal:
diagonal = \(√32\)
Step 6: Round to the nearest tenth: The square root of 32 is approximately 5.7.
Therefore, the diagonal distance in Sally's bedroom is about 5.7 meters.