Solution:
Given:
where;
![\begin{gathered} l=20ft \\ h=16ft \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/105axf8a9ibfjc8xsvlfvo4hseldtw2e93.png)
A right triangle can be extracted from the image above,
Applying the Pythagoras theorem to the right triangle,
![\begin{gathered} \text{hypotenuse}^2=\text{opposite}^2+\text{adjacent}^2 \\ \\ \text{Thus,} \\ l^2=h^2+w^2 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/high-school/3jdtsz6l7ds4wciqx12kn0amtx298qsjg1.png)
To find w, substitute the known values into the formula,
![\begin{gathered} l^2=h^2+w^2 \\ 20^2=16^2+w^2 \\ 400=256+w^2 \\ 400-256=w^2 \\ 144=w^2 \\ w=\sqrt[]{144} \\ w=\pm12 \\ Si\text{nce the problem is on the distance to hold the base of the ladder, we pick the positive value only.} \\ \text{Thus,} \\ w=12ft \end{gathered}]()
Therefore, the distance from the wall that the base of the ladder should be while they climb back in is 12 feet.
Hence, option D is the correct answer.