The length and width of the garden are 47 ft and 21 ft respectively.
<u><em>Explanation</em></u>
Suppose, the width of the garden is
feet.
As the garden is 5 feet longer than twice its width, so the length will be: ![(2x+5) feet](https://tex.z-dn.net/?f=%282x%2B5%29%20feet)
So, the area of the garden ![= length*width=x(2x+5)ft^2](https://tex.z-dn.net/?f=%3D%20length%2Awidth%3Dx%282x%2B5%29ft%5E2)
Now, the garden has a sidewalk 3 feet wide on two of its sides. That means, the length of the garden including the sidewalk
and the width including the sidewalk ![=(x+3)ft](https://tex.z-dn.net/?f=%3D%28x%2B3%29ft)
Given that, the area of the sidewalk is 213 ft². So the equation will be.....
![(2x+8)(x+3)-x(2x+5)=213\\ \\ 2x^2+14x+24-2x^2-5x=213\\ \\ 9x+24=213\\ \\ 9x=189\\ \\ x=\frac{189}{9}=21](https://tex.z-dn.net/?f=%282x%2B8%29%28x%2B3%29-x%282x%2B5%29%3D213%5C%5C%20%5C%5C%202x%5E2%2B14x%2B24-2x%5E2-5x%3D213%5C%5C%20%5C%5C%209x%2B24%3D213%5C%5C%20%5C%5C%209x%3D189%5C%5C%20%5C%5C%20x%3D%5Cfrac%7B189%7D%7B9%7D%3D21)
So, the width of the garden is 21 feet and the length is ![(2*21+5)ft= 47 ft](https://tex.z-dn.net/?f=%282%2A21%2B5%29ft%3D%2047%20ft)