Use the image to answer the question.

Question

An illustration shows a three dimensional rectangular prism with labeled parts. The top, front and right sides are visible. The bottom, left, and rear sides are not visible, but their positions are indicated by dashed lines. The vertical edge joining the front and left sides is labeled h. A right angle is indicated where that edge meets the front base edge. The front base edge is labeled l. A right angle is indicated where that edge meets the right base edge. The right base edge is labeled w. Two dotted lines extend from the vertex at the back right side of the prism through the interior. The first dotted line extends up to the vertex at the front left side and is labeled d. The second dotted line extends diagonally across the base to the vertex at the front left side where the perpendicular height line meets the base edge and is labeled x.

Given l=30 in.
, w=20 in.
, h=18 in.
, and x=36.1 in.
, find the length of d
. Round the answer to the nearest tenth.

(1 point)
in.
Remaining Attempts : 3

Answer 1

To find the length of \( d \), which represents the space diagonal of the rectangular prism, we can use the formula for the space diagonal of a rectangular prism, given by:

\[ d = \sqrt{l^2 + w^2 + h^2} \]

Substituting the values for \( l \), \( w \), and \( h \):

• \( l = 30 \) in
• \( w = 20 \) in
• \( h = 18 \) in

We calculate \( d \) as follows:

1. Calculate \( l^2 \): \[ l^2 = 30^2 = 900 \]

2. Calculate \( w^2 \): \[ w^2 = 20^2 = 400 \]

3. Calculate \( h^2 \): \[ h^2 = 18^2 = 324 \]

4. Now, add these three values together: \[ l^2 + w^2 + h^2 = 900 + 400 + 324 = 1624 \]

5. Finally, take the square root to find \( d \): \[ d = \sqrt{1624} \]

Calculating the square root gives: \[ d \approx 40.31 \]

Rounding to the nearest tenth: \[ d \approx 40.3 , \text{in.} \]

Thus, the length of \( d \) is approximately 40.3 in.