A pencil sits in a pencil holder that is a rectangular prism. The pencil sits on a diagonal inside the box.
Find the length of the pencil.
The rectangular prism measures 8 cm in height, 4 cm in length, and 3 cm in width.
Use the Pythagorean theorem.
Answer (3)
t h e l e n g t h o f t h e p e n c i l = t h e l e n g t h o f t h e d ia g o na l = . = a 2 + b 2 + c 2 a 2 + b 2 + c 2 = 8 2 + 4 2 + 3 2 = 64 + 16 + 9 = 89 ≈ 9.43 [ c m ] A n s . t h e l e n g t h o f t h e p e n c i l i s ab o u t 9.43 [ c m ]
Diagonal of rectanglular prism = √a² + b² + c²
= √8² + 4² + 3²
= √89
= 9.43
Thus, the pencil is 9.43 cm long.
The length of the pencil, which is the diagonal of the box, is calculated to be approximately 9.43 cm using the Pythagorean theorem. We used the box's dimensions of 8 cm, 4 cm, and 3 cm to arrive at this conclusion. Hence, the formula d = h 2 + l 2 + w 2 provided a direct way to find the diagonal length.
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