Since the length and breadth are not given, the length of the diagonal can be anything from the smallest fraction to the largest number of units.
I guess the diagonal length given is from one corner of the box to the opposite corner reached by traversing one length side, one edge side and one height side. Using Pythagoras, the length of the diagonal of the base (length by width) can be found. Using this diagonal and the height of the box, the diagonal from corner-to-opposite-corner of the box can be found using Pythagoras. However, as this [longer] diagonal is know, the height can be found by rearranging this last use of Pythagoras: Diagonal_base2 = length2 + width2 Diagonal_box2 = diagonal_base2 + height2 ⇒ height = √(diagonal_box2 - diagonal_base2 ) = √(diagonal_box2 - (length2 + width2)) = √(diagonal_box2 - length2 - width2) Now that the formula has been derived, plugging in (substituting) the various lengths will allow the height to be calculated.
8.9
The long diagonal will be sqrt(7500) cm = 86.60 cm (to 2 dp)
A box has no equation. There are different equations for its volume, its surface area, the longest (principal) diagonal.
If it is a 2-D box then 70.71
Since the length and breadth are not given, the length of the diagonal can be anything from the smallest fraction to the largest number of units.
I guess the diagonal length given is from one corner of the box to the opposite corner reached by traversing one length side, one edge side and one height side. Using Pythagoras, the length of the diagonal of the base (length by width) can be found. Using this diagonal and the height of the box, the diagonal from corner-to-opposite-corner of the box can be found using Pythagoras. However, as this [longer] diagonal is know, the height can be found by rearranging this last use of Pythagoras: Diagonal_base2 = length2 + width2 Diagonal_box2 = diagonal_base2 + height2 ⇒ height = √(diagonal_box2 - diagonal_base2 ) = √(diagonal_box2 - (length2 + width2)) = √(diagonal_box2 - length2 - width2) Now that the formula has been derived, plugging in (substituting) the various lengths will allow the height to be calculated.
36
8.9
The long diagonal will be sqrt(7500) cm = 86.60 cm (to 2 dp)
A box has no equation. There are different equations for its volume, its surface area, the longest (principal) diagonal.
Cool question ! Answer - half it then cube it to prove it - an example for you if cube diagonal (not square diagonal) is 100, then using pythagoras theorm the square diagonal = 70.71068, If square the square diagonal = 70.71068, then using pythagoras theorm the side length = 50 therefore the volume = 50 ^ 3 = 25000 units works with any numbers
the equation is L^2= w^2 + h^2 + l^2 where L= length of diagonal, w=width, h=height, and l= length, L= sqrt( (30)^2 + (24)^2 + (18)^2)= (approx) 42.2 cm
Use Pythagoras' theorem to find the length of the outer diagonal and then use this as the base for the inner diagonal (the longest length of the cube) 82+82 = 128 and the square root of this is 11.3137085 cm 11.31370852+82 = 192 and the square root of this is 13.85640646 cm The longest pencil is 13.85640646 or just under 14 cm
It has to land in the opposite diagonal service box (because you face the opposite diagonal service box when you are serving).
The longest ski pole to fit would lie diagonally. The length of the diagonal can be found by the pythagorean theorem.d=sqrt(1202+252)d ~= 122.58 cm