Question

use the information to answer the question.
a rectangular prism is shown with the dimensions.
image of rectangular prism with labels a, b, c, d, dimensions 7 in., 24 in., 10 in.
*not drawn to scale
what is the distance between a and d? enter the answer in the box. round the answer to the nearest hundredth of an inch.
box inches

Explanation:

Step1: Identify the right triangle

In the rectangular prism, the distance from \( B \) to \( D \) can be found first using the base rectangle with length \( 24 \) in and width \( 10 \) in. Then, triangle \( ABD \) is a right triangle with legs \( AB = 7 \) in and \( BD \), and hypotenuse \( AD \).
First, find \( BD \) using the Pythagorean theorem for the base: \( BD=\sqrt{24^{2}+10^{2}} \)
\( BD=\sqrt{576 + 100}=\sqrt{676}=26 \) in.

Step2: Find \( AD \) using Pythagorean theorem

Now, in triangle \( ABD \), \( AB = 7 \) in, \( BD = 26 \) in, so \( AD=\sqrt{7^{2}+26^{2}} \)
\( AD=\sqrt{49+676}=\sqrt{725}\approx26.9258 \)

Step3: Round to nearest hundredth

Rounding \( 26.9258 \) to the nearest hundredth gives \( 26.93 \).

Answer:

\( 26.93 \)