2. Find the length of the diagonal of the cuboid of measurements 6cm.8cm and 10cm
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In general, the length of the diagonal (d) of a right rectangular prism (a rectangular box) with length (l), width (w), and height (h) is given by the following 3-dimensional form of the pythagorean theorem:
d2 = l2 + w2 + h2
To solve for d, take the square root of both sides of this equation:
√(d2) = √(l2 + w2 + h2)
d = √(l2 + w2 + h2)
Since the rectangular box in question has the dimensions 6 cm x 8 cm x 10 cm, then the length of the diagonal is as follows:
d = √(62 + 82 + 102)
d = √(36 + 64 + 100)
d = √(200)
d = √(100)·√(2)
d = 10√(2)
Therefore, the length of the diagonal of this rectangular box is 10√2 cm.
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