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. ____ in.

Answer 1

To find the length $d$, we can use the Pythagorean theorem in a three-dimensional context. The formula for the diagonal $d$ of a rectangular box with length $l$, width $w$, and height $h$ is given by:

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

Given the dimensions:

• $l=30$ in
• $w=20$ in
• $h=18$ in

We can substitute these values into the formula:

$$d=\sqrt{{30}^2+{20}^2+{18}^2}$$

Calculating each term:

$${30}^2=900$$ $${20}^2=400$$ $${18}^2=324$$

Now, summing these values:

$$900+400+324=1624$$

Now, taking the square root:

$$d=\sqrt{1624}\approx 40.249$$

Rounding to the nearest tenth:

$$d\approx 40.2\text{ in}$$

Thus, the length of $d$ is approximately 40.2 in.