To solve for the length and width of the rectangular garden, we can set up a system of equations. By using the formula for the area of a rectangle and simplifying the equation, we can find the values for the width and length. The width of the garden is 13 feet and the length is 59 feet.
Step-by-step explanation:
To solve this problem, we can set up a system of equations:
Let x be the width of the rectangular garden.
According to the problem, the length of the garden is 5 times its width minus 6 feet. So the length can be represented as 5x - 6.
We know that the area of a rectangle is equal to its length times its width. In this case, the area is given as 317 square feet. So we have the equation:
x(5x - 6) = 317
Simplifying and rearranging the equation, we get:
5x^2 - 6x - 317 = 0
We can solve this quadratic equation using factoring, completing the square, or the quadratic formula. After solving, we find that x = 13 and x = -6.4. Since the width cannot be negative, the width of the garden is 13 feet.
Substituting the width back into the equation for length, we get:
length = 5(13) - 6 = 65 - 6 = 59 feet.