A fast approach to solving this problem is to use the “Super Pythagorean theorem,” which states that the diagonal of any rectangular box
is d in the following formula:
d2 = l2 + w2 + h2
where l, w, and h are the length, width, and height of the box, respectively.
Plugging in the given information yields:
d2 = 62 + 82 + 102
d2 = 36 + 64 + 100
d2 = 200
Alternatively, if you don’t remember the Super Pythagorean, apply the normal
Pythagorean theorem twice. To find the diagonal of the box, first find the
diagonal of one of the sides. Use the bottom side of the figure below as the
base:
Applying the
Pythagorean theorem:
c2 = a2 + b2
c2 = 62 + 82
c2 = 36 + 64
c2 = 100
c = 10
From here, draw the diagonal of the box and apply the Pythagorean theorem
again to the vertically oriented triangle with legs 10 and 10 again
d2 = 102 + 102
d2 = 100 + 100
d2 = 200
d=10sqrt(2)