Question

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.)

Answer 1

15.36 cm

Step-by-step 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