Suppose that there is a rectengular box with a length of 8 centimeters a width of 6 centimeters and a height of 4 centimeters.Find the length of a diagonal from a lower corner to the upper corner diagonally opposite.
Answer is 10.8 centimeters
d^2 = 8^2 + 6^2 + 4^2 = 116
d=√116 = appr 10.8
To find the length of the diagonal from a lower corner to the upper corner diagonally opposite, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the length, width, and height of the rectangular box form the three sides of a right-angled triangle. We can choose the length and width as the two sides and calculate the diagonal length using the formula:
diagonal length = √(length² + width² + height²)
Substituting the given values:
diagonal length = √(8² + 6² + 4²)
= √(64 + 36 + 16)
= √116
≈ 10.8 centimeters
Therefore, the length of the diagonal from a lower corner to the upper corner diagonally opposite is approximately 10.8 centimeters.