[tex]P= \frac{ {a}^{2} \sqrt{3} }{4} \\ \\ 100 \sqrt{3} = \frac{ {a}^{2} \sqrt{3} }{4} | \times 4 \\ \\ 400 \sqrt{3} = {a}^{2} \sqrt{3} \rightarrow a = 20 \\ \\ h = \frac{a \sqrt{3} }{2} \\ \\ h = \frac{20 \sqrt{3} }{2} = 10 \sqrt{3} \\ [/tex]
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[tex]P= \frac{ {a}^{2} \sqrt{3} }{4} \\ \\ 100 \sqrt{3} = \frac{ {a}^{2} \sqrt{3} }{4} | \times 4 \\ \\ 400 \sqrt{3} = {a}^{2} \sqrt{3} \rightarrow a = 20 \\ \\ h = \frac{a \sqrt{3} }{2} \\ \\ h = \frac{20 \sqrt{3} }{2} = 10 \sqrt{3} \\ [/tex]