Question

let the longest diagonal of a closed rectangular box be 6 units in length. If the lemgths of its edges are all integers, find the volume of the box.

Answer 1

Answer:

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.