Question

1. the dimensions of a rectangular prism are 8 in, 15 in, and 20 in. what is the space diagonal?

a. 26.83 in
b. 28.12 in
c. 26.25 in
d. 29.14 in

Explanation:

Step1: Recall the formula for space - diagonal

The formula for the space - diagonal $d$ of a rectangular prism with length $l$, width $w$, and height $h$ is $d=\sqrt{l^{2}+w^{2}+h^{2}}$. Here, $l = 8$, $w = 15$, and $h = 20$.

Step2: Calculate the squares of the dimensions

$l^{2}=8^{2}=64$, $w^{2}=15^{2}=225$, $h^{2}=20^{2}=400$.

Step3: Sum the squares

$l^{2}+w^{2}+h^{2}=64 + 225+400=689$.

Step4: Find the square - root

$d=\sqrt{689}\approx26.25$ in.

Answer:

C. 26.25 in