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
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