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## Find the length of a diagonal of a rectangular box whose edges are 6cm, 8cm, and 10 cm

Find the length of a diagonal of a rectangular box whose edges are 6cm, 8cm, and 10 cm. Write all radicals in simplest form

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.

Create a diagonal for the base of the rectangle box and it will be 10 cm long using the right triangle - Pythagorean therm  a^2+b^2 = C^2

Now you will see that the diagonal of the base = 10 cm and the height of the box also = 10 cm

Now again do Pythagorean therm a^2+b^2 = C^2

and the length of the diagonal of the rectangular box = 10√2