Swimming pool 7

The perimeter of a rectangular swimming pool is 20 4/5 meters. Its length is thrice its width. What is the length of the pool? What is its width?

Correct answer:

a =  7 ⁴⁄₅ = 39/5 m
b =  2 ³⁄₅ = 13/5 m

Step-by-step explanation:

$$\begin{gathered} p=20\frac{4}{5}=20+\frac{4}{5}=\frac{20\cdot 5+4}{5}=\frac{100+4}{5}=\frac{104}{5}=20.8\text{m} \\ a=3b \\ p=a+b+a+b=2a+2b=2(a+b) \\ p=2a+2/3\cdot a \\ 20.8=2a+2/3\cdot a \\ 20.8=2\cdot a+2/3\cdot a \\ 8a=62.4 \\ a=\frac{62.4}{8}=7.8 \\ a=\frac{39}{5}=7.8=\frac{39}{5}\text{m}=7\frac{4}{5}\text{m}=7.8\text{m} \end{gathered}$$

$$\begin{gathered} b=a/3=7.8/3=\frac{13}{5}=2.6=\frac{13}{5}\text{m}=2.6\text{m} \\ \text{ Verifying Solution: } \\ {p}_2=2\cdot (a+b)=2\cdot (7.8+2.6)=\frac{104}{5}=20.8\text{m} \end{gathered}$$

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