Questions: The width of a rectangle is 4 less than twice its length. If the area of the rectangle is 103 cm^2, what is the length of the diagonal? The length of the diagonal is cm. Give your answer to 2 decimal places.

Determine the dimensions of the rectangle based on the given area.

Express the width in terms of the length.

The width \( w \) is given by the equation \( w = 2l - 4 \), where \( l \) is the length.

Set up the equation for the area of the rectangle.

The area \( A \) is given by \( A = l \cdot w = 103 \). Substituting for \( w \), we have \( l(2l - 4) = 103 \).

Solve for the length \( l \).

Rearranging gives the equation \( 2l^2 - 4l - 103 = 0 \). Using the quadratic formula, we find \( l = 1 - \frac{\sqrt{210}}{2} \) (the positive root is not valid as it leads to a negative width).

Calculate the width \( w \).

Substituting \( l \) back into the width equation gives \( w = -\sqrt{210} - 2 \), which is also invalid as it leads to a negative value.

The dimensions of the rectangle cannot be valid due to negative values.

Calculate the length of the diagonal of the rectangle.

Use the Pythagorean theorem to find the diagonal \( d \).

The diagonal is given by \( d = \sqrt{l^2 + w^2} \). Substituting the values, we find \( d = \sqrt{(1 - \frac{\sqrt{210}}{2})^2 + (-\sqrt{210} - 2)^2} \).

Simplify the expression for the diagonal.

After simplification, we find \( d \approx 17.634458603500374 \).

Round the diagonal to two decimal places.

Thus, the length of the diagonal is \( d \approx 17.63 \) cm.

The length of the diagonal is \( \boxed{17.63} \) cm.

The dimensions of the rectangle cannot be valid due to negative values.
The length of the diagonal is \( \boxed{17.63} \) cm.