A garden has an area of $266 \mathrm{ft}^{2}$. Its length is $5 \mathrm{ft}$ more than its width. What are the dimensions of the garden? The width of the garden is $\square \square \nabla$ and the length of the garden is $\square \square \nabla$ (Simplify your answers.) example Get more help -

Step 1 ：Let's denote the width of the garden as \(w\) and the length as \(l\). We know that the area of the garden is 266 square feet and the length is 5 feet more than the width. So we can write these facts as two equations: \(l = w + 5\) and \(l \times w = 266\).

Step 2 ：Substitute \(l\) from the first equation into the second equation, we get \(w \times (w + 5) = 266\). This is a quadratic equation in terms of \(w\).

Step 3 ：Solving this quadratic equation, we get two solutions for \(w\): -19 and 14. However, the width of a garden cannot be negative. Therefore, the width of the garden is 14 feet.

Step 4 ：Substitute \(w = 14\) into the first equation, we get \(l = 14 + 5 = 19\). So the length of the garden is 19 feet.

Step 5 ：Final Answer: The width of the garden is \(\boxed{14}\) feet and the length of the garden is \(\boxed{19}\) feet.