Louis

Louis wants to carpet the rectangular floor of his basement. The basement has an area of 5,120 square feet. The width of the basement is 4/5 its length. What is the length of Louis's basement?

Correct answer:

x =  80 ft

Step-by-step explanation:

$$\begin{gathered} A=5120{\text{ft}}^2 \\ y=\frac{4}{5}\cdot x \\ A=xy \\ A=x\cdot \frac{4}{5}\cdot x \\ x=\sqrt{A\cdot \frac{5}{4}}=\sqrt{5120\cdot \frac{5}{4}}=80=80\text{ft} \\ \text{ Verifying Solution: } \\ y=\frac{4}{5}\cdot x=\frac{4}{5}\cdot 80=\frac{4\cdot 80}{5}=\frac{320}{5}=64\text{ft} \\ {A}_2=x\cdot y=80\cdot 64=5120{\text{ft}}^2 \end{gathered}$$

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