Garden

The area of a square garden is 2/9 of triangle garden with sides 160 m, 100 m, and 100 m.

How many meters of fencing need to fence a square garden?

Correct answer:

o =  131 m

Step-by-step explanation:

$$\begin{gathered} k={\displaystyle \frac{2}{9}}\doteq 0.2222 \\ a=160\doteq 32.6599\text{ m } \\ b=100\text{ m } \\ c=b=100\text{ m } \\ h=\sqrt{b^2-(a\mathrm{/}2{)}^2}=\sqrt{100^2-(32.6599\mathrm{/}2{)}^2}=60\text{ m } \\ {S}_1={\displaystyle \frac{a\cdot h}{2}}={\displaystyle \frac{32.6599\cdot 60}{2}}=4800{\text{m}}^2 \\ {S}_2=k\cdot S_1=0.2222\cdot 4800={\displaystyle \frac{3200}{3}}\doteq 1066.6667{\text{m}}^2 \\ {S}_2=a^2 \\ a=\sqrt{S_2}=\sqrt{1066.6667}\doteq 32.6599\text{ m } \\ o=4\cdot a=4\cdot 32.6599\doteq 130.6395=131\text{ m } \\ \text{ Verifying Solution: } \\ {o}_2=2\cdot \sqrt{2\mathrm{/}9\cdot 160\cdot \sqrt{4\cdot 100\cdot 100-160\cdot 160}}\doteq 130.6395 \end{gathered}$$

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