Question

what is the measurement of the longest line segment in a right rectangular prism that is 12.6 centimeters long, 3.2 centimeters wide, and 6 centimeters tall?
the longest line segment is \\(\square\\) cm.
(round to the nearest tenth as needed.)

Explanation:

Step1: Recall space diagonal formula

The longest segment in a right rectangular prism is its space diagonal, calculated by:
$$d = \sqrt{l^2 + w^2 + h^2}$$
where $l=12.6$ cm, $w=3.2$ cm, $h=6$ cm.

Step2: Calculate squared side lengths

$$l^2 = 12.6^2 = 158.76$$
$$w^2 = 3.2^2 = 10.24$$
$$h^2 = 6^2 = 36$$

Step3: Sum the squared values

$$158.76 + 10.24 + 36 = 205$$

Step4: Compute square root, round to tenth

$$d = \sqrt{205} \approx 14.3$$

Answer:

14.3 cm