Problem

A rectangular vegetable garden will have a width that is 4 feet less than the length, and an area of 140 square feet. If $x$ represents the length, then the length can be found by solving the equation: \[ x(x-4)=140 \] What is the length, $\mathrm{x}$, of the garden? The length is feet. The solution is

Solution

Step 1 :The problem is asking for the length of the garden, which is represented by x. The equation given is a quadratic equation, which can be solved by factoring, completing the square, or using the quadratic formula. In this case, the equation is already in the form of a product equal to a constant, so it can be solved by factoring.

Step 2 :Set up the equation: \(x(x - 4) = 140\)

Step 3 :Solve the equation to find the possible values of x. The solutions to the equation are -10 and 14.

Step 4 :However, since the length of a garden cannot be negative, discard the negative solution.

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

From Solvely APP
Source: https://solvelyapp.com/problems/24632/

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