Find the diagonal of the rectangular solid with given measurements: l=8,w=4,h=2
D^2 = L^2+W^2+h^2,
D^2 = 8^2+4^2+2^2 = 84,
D = 9.17= Length of diagonal.
To find the diagonal of the rectangular solid, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length 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, we can consider the diagonal of the rectangular solid as the hypotenuse of a right triangle, with the length, width, and height of the rectangular solid as its sides.
Using the given measurements, we have:
Length (l) = 8
Width (w) = 4
Height (h) = 2
We need to find the length of the diagonal (d).
Applying the Pythagorean theorem:
d² = l² + w² + h²
Substituting the given measurements:
d² = 8² + 4² + 2²
d² = 64 + 16 + 4
d² = 84
To find the value of d, we take the square root of both sides:
d = √84
Calculating the square root of 84, we get approximately:
d ≈ 9.165
Therefore, the diagonal of the rectangular solid is approximately 9.165 units.