We know that
• The length is 7 meters more than double the width.
,
• The area is 99 square meters.
First, we express the relationship between the length and the width.

We know that the area is

Replacing the first expression, and the area.

Let's solve for w.

Now, we use the quadratic formula.
![w_(1,2)=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}](https://img.qammunity.org/2023/formulas/mathematics/college/6r67siwjsujm9iuz3yblp7ykx8e1ze0f9n.png)
Where a = 2, b = 7, and c = -99. Let's replace all these values in the formula.
![\begin{gathered} w_(1,2)=\frac{-7\pm\sqrt[]{7^2-4\cdot2\cdot(-99)}}{2(2)}=\frac{-7\pm\sqrt[]{49+792}}{4} \\ w_(1,2)=\frac{-7\pm\sqrt[]{841}}{4}=(-7\pm29)/(4) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/9noqma6vlqc1atm05f9vg9p9e4f5s0d6nj.png)
Now, we rewrite it into two equations.

The width is 5.5 meters because it can't be represented by a negative number.
We use the width to find the length.

The length is 18 meters.
Therefore, the dimensions are 5.5 meters wide and 18 meters in length.