Final answer:
To find the dimensions of the rectangular garden, we solve a quadratic equation by setting up an equation using the given information. We then solve for the width and calculate the length using the given relationship. The dimensions of the rectangular garden are 4 units wide and 9 units long.
Step-by-step explanation:
To solve this problem, let's first let x represent the width of the rectangular garden. Since the length is 5 more than the width, we can express the length as x + 5. The area of a rectangle is given by the formula length × width. We can set up the equation:
x(x + 5) = 36
Expanding and rearranging the equation, we get a quadratic equation:
x^2 + 5x - 36 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula to find the values of x, which represent the width. Once we have the width, we can calculate the length by adding 5.
After solving the equation, we find that the width is approximately 4 units and the length is approximately 9 units. Therefore, the dimensions of the rectangular garden are 4 units wide and 9 units long.