A farmer wished to construct a rectangular fence with one side along a barn. The farmer has 240 feet of fence and wished to have the length be 3 times the width. Find the dimensions of the fence.
Question
A farmer wished to construct a rectangular fence with one side along a barn. The farmer has 240 feet of fence and wished to have the length be 3 times the width. Find the dimensions of the fence.
Solution
Sure, let's solve this step by step.
Step 1: Define the variables Let's denote the width of the fence as W and the length as L. According to the problem, the length is three times the width, so we can say L = 3W.
Step 2: Set up the equation The farmer has 240 feet of fence. This fence will be used for two widths and one length (since one side is along a barn and doesn't need fencing). So, the equation will be 2W + L = 240.
Step 3: Substitute L in the equation We know that L = 3W, so we can substitute this into the equation: 2W + 3W = 240.
Step 4: Solve for W Combine like terms: 5W = 240. Divide each side by 5 to solve for W: W = 240 / 5 = 48 feet.
Step 5: Solve for L Substitute W = 48 into the equation L = 3W to find L: L = 3 * 48 = 144 feet.
So, the width of the fence is 48 feet and the length is 144 feet.
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