A real estate purveyor purchases a 60,000 square foot (ft^(2)) warehouse and decides to turn it into a storage facility. The warehouse's width is exactly (2)/(3) of its length. What is the warehouse's width? Round your answer to the nearest foot.

Question

A real estate purveyor purchases a 60,000 square foot  (ft^(2)) warehouse and decides to turn it into a storage facility. The warehouse's width is exactly  (2)/(3) of its length. What is the warehouse's width? Round your answer to the nearest foot.

Bytelearn · Accepted Answer

Identify Relationship: Identify the relationship between the width and length of the warehouse. The width is (2/3) of the length. This means if we let L represent the length, then the width W can be represented as W = (2/3)L.Set Up Equation: Set up the equation for the area of the warehouse using the relationship between width and length. The area A of the warehouse is given by A = L * W. We know the area is 60,000 square feet, so we can write the equation as 60,000 = L * (2/3)L.Solve for Area: Solve the equation for L^2. To find L, we need to solve for L^2 first. We can rewrite the equation as 60,000 = (2/3)L^2. Multiplying both sides by (3/2) gives us (3/2) * 60,000 = L^2.Calculate L^2: Calculate L^2. Now we calculate L^2 by multiplying (3/2) by 60,000. L^2 = (3/2) * 60,000 = 90,000.Solve for L: Solve for L. To find L, we take the square root of L^2. L = sqrt(90,000). L is approximately equal to 300 feet (since sqrt(90,000) = 300).Calculate Width: Calculate the width W using the relationship W = (2/3)L. Now that we know L is approximately 300 feet, we can find W by multiplying (2/3) by L. W = (2/3) * 300 = 200 feet.Round Answer: Round the answer to the nearest foot. The calculated width W is 200 feet, which is already a whole number, so no rounding is necessary.

A real estate purveyor purchases a $60$ , $000$ square foot $\left(\mathrm{ft}^{2}\right)$ warehouse and decides to turn it into a storage facility. The warehouse's width is exactly $\frac{2}{3}$ of its length. What is the warehouse's width? Round your answer to the nearest foot.

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