Question

Find the length of the line segment inside the rectangular prism.

Answer 1

To find the length of the yellow segment, we have to use Pythagorean's Theorem. But first, we have to find the length of the black line at the bottom.

$c^2=a^2+b^2$

Where a = 4ft and b = 9ft.

$\begin{gathered} c^2=4^2+9^2 \\ c^2=15+81 \\ c=\sqrt[]{96} \\ c\approx9.8 \end{gathered}$

So, the length of the black segment is 9.8 feet.

Now, we find the yellow line length

$c^2=a^2+b^2$

Where a = 4 and b = 6.

$\begin{gathered} c^2=4^2+6^2 \\ c^2=16+36 \\ c^2=52 \\ c=\sqrt[]{52} \\ c\approx7.2 \end{gathered}$

Therefore, the length of the yellow line is 7.2 feet.