Full solution

Q. 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.

Identify Relationship: Identify the relationship between the width and length of the warehouse. $\newline$ The width is $(\frac{2}{3})$ of the length. This means if we let $L$ represent the length, then the width $W$ can be represented as $W = (\frac{2}{3})L$ .
Set Up Equation: Set up the equation for the area of the warehouse using the relationship between width and length. $\newline$ The area $A$ of the warehouse is given by $A = L \times W$ . We know the area is $60,000$ square feet, so we can write the equation as $60,000 = L \times (\frac{2}{3})L$ .
Solve for Area: Solve the equation for $L^2$ . $\newline$ To find $L$ , we need to solve for $L^2$ first. We can rewrite the equation as $60,000 = \left(\frac{2}{3}\right)L^2$ . Multiplying both sides by $\left(\frac{3}{2}\right)$ gives us $\left(\frac{3}{2}\right) \times 60,000 = L^2$ .
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. $\newline$ 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 $W = \frac{2}{3}L$ . Now that we know $L$ is approximately $300$ feet, we can find $W$ by multiplying $\frac{2}{3}$ by $L$ . $W = \frac{2}{3} \times 300 = 200$ 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.