Question

A box in the shape of a rectangular prism has the dimensions shown. To the nearest tenth of a centimeter, how many centimeters long is the interior diagonal of the box?

A rectangular prism with a base that measures 6 centimeters by 8 centimeters, and a height of 11 centimeters. A dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the same base. Another dashed diagonal line is drawn from one vertex of the base to the opposite vertex of the other base.

Answer 1

14.9 cm

Explanation:

You want the length of the interior diagonal of a rectangular prism with dimensions 6 cm, 8 cm, and 11 cm.

Space diagonal

The length of the space diagonal of a rectangular prism is given by ...

d = √(L² +W² +H²)

d = √(6² +8² +11²) = √221 ≈ 14.9 . . . cm

The length of the interior diagonal is about 14.9 cm.

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Additional comment

The dashed lines in the figure are to help you understand you can find the length using the Pythagorean theorem twice. The base diagonal will be √(a²+b²), and the space diagonal will be ...

d = √((√(a²+b²))² +c²) = √(a² +b² +c²) . . . . as above

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