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The length of a rectangular garden is 6 feet less than 5 times its width.

Its area is 317 square feet. what is the length and width

User Ninjasense
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1 Answer

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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.

User Alex Pollan
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