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

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

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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*:

**d**^{2}** = l**^{2}** + w**^{2}** + h**^{2}

To solve for d, take the square root of both sides of this equation:

√(d^{2}) = √(l^{2} + w^{2} + h^{2})

**d = √(l**^{2}** + w**^{2}** + h**^{2}**)**

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 = √(6**^{2}** + 8**^{2}** + 10**^{2}**)**

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

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