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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 rectangle prism measures 8cm height 4cm length and 3cm width) Pythagorean theorem

Sagot :

Diagonal of rectanglular prism = √a² + b² + c²

= √8² + 4² + 3²

= √89

= 9.43

Thus, the pencil is 9.43 cm long.
[tex]the\ length\ of\ the\ pencil= the\ length\ of\ the\ diagonal=\\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \sqrt{a^2+b^2+c^2} \\\\\sqrt{a^2+b^2+c^2} = \sqrt{8^2+4^2+3^2} = \sqrt{64+16+9} = \sqrt{89}\approx9.43\ [cm] \\\\Ans.\ the\ length\ of\ the\ pencil\ is\ about\ 9.43\ [cm][/tex]