$\"\"$

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The volume of the rectungular prism is $\"\"$ .

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Height of the tunnel is $\"\"$ feet more than $\"\"$ of its width, hence height $\"\"$ .

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Length of the tunnel is $\"\"$ feet more than $\"\"$ times of its width, $\"\"$ .

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Subustiute these values into the equation for volume of the tunnel $\"\"$ . $\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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The volume of the tunnel is $\"\"$ cubic feet.

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Subustiute $\"\"$ in the equation $\"\"$ and solve for $\"\"$ .

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$\"\"$

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The obtained polynomial equation is $\"\"$ .

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The above polynomial has $\"\"$ sign variation. so , it has $\"\"$ positive real zero.

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$\"\"$

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Graph :

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Draw the coordinate plane.

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Graph the function $\"\"$ .

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$\"\"$

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Observe the graph:

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The function $\"\"$ touches the $\"\"$ axis at $\"\"$ .

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$\"\"$

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Synthetic Division:

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The function is $\"\"$ .

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Perform the synthetic division method by testing $\"\"$ .

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$\"\"$

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$\"\"$ must be a positive value because ,the above polynomial has $\"\"$ sign variation. so , it has $\"\"$ posotive real zero.

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$\"\"$

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Since $\"\"$ only has $\"\"$ positive real zero.Width of the tunnel is $\"\"$ feet.

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Therwfore width of the tunnel , $\"\"$ $\"\"$ feet.

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Height of the tunnel, $\"\"$ .

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$\"\"$

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Length of the tunnel is $\"\"$ .

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$\"\"$

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$\"\"$

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Width of the tunnel is $\"\"$ $\"\"$ feet.

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Height of the tunnel is $\"\"$ feet.

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Length of the tunnel is $\"\"$ feet.