$\"\"$

\

Length of the trough $\"\"$ ft.

\

Height of the isosceles of the triangle is $\"\"$ ft.

\

Side of the triangle is $\"\"$ ft.

\

Trough is being filled with water at a rate of $\"\"$ ft³/min.

\

Thus, $\"\"$ .

\

\

Diagram of the situation at any time $\"\"$ :

\

\

$\"\"$

\

Consider at any time $\"\"$ , the width of the water level is $\"\"$ .

\

And height of the water is $\"\"$ .

\

From the property of the similar triangles.

\

$\"\"$

\

Volume of the above trough is $\"\"$ .

\

Here, $\"\"$ and $\"\"$ .

\

$\"\"$

\

Differentiate on each side with respect to $\"\"$ .

\

$\"\"$

\

Find the rate at which water level is rising when it is $\"\"$ inches deep.

\

Thus, $\"\"$ .

\

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

\

$\"\"$

\

\

Rate at which water level rising is $\"\"$ ft/min.

\

\

$\"\"$

\

Rate at which water level rising is $\"\"$ ft/min.