$\"\"$

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

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

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

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

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Thus, $\"\"$ .

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

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$\"\"$

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

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

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From the property of the similar triangles.

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$\"\"$

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

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

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$\"\"$

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

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$\"\"$

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

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Thus, $\"\"$ .

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

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$\"\"$

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

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$\"\"$

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