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The rectangular prism shown has a length of 10 cm, a width of 10 cm, and a height of 6 cm. Find the length of the inner diagonal AD of the prism. Note that AD is the hypotenuse of right triangle ACD. (Round your answer to the nearest hundredth.)

The rectangular prism shown has a length of 10 cm a width of 10 cm and a height of 6 cm Find the length of the inner diagonal AD of the prism Note that AD is th class=

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sqdancefan

Answer:

15.36 cm

Explanation:

The Pythagorean theorem tells you ...

... AC² = AB² + BC² . . . . . relation for face diagonal

... AD² = AC² + CD² . . . . . relation for space diagonal

Subsituting the expression for AC² given by the first equation, the second equaiton becomes ...

... AD² = AB² + BC² + CD²

... AD² = (100 cm²) + (100 cm²) + (36 cm²) = 236 cm²

Taking the square root, we have ...

... AD = √236 cm = 2√59 cm

... AD ≈ 15.36 cm

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