Răspuns:
[tex]a)a = 25 \sqrt{3} \\ \frac{ {l}^{2} \sqrt{3} }{4} = 25 \sqrt{3} \\ {l}^{2} \sqrt{3} = 25 \sqrt{3} \times 4 \\ {l}^{2} \sqrt{3} = 100 \sqrt{3} \\ { l}^{2} = 100 \sqrt{3} \div \sqrt{3} \\ {l}^{2} = 100 \\ l = \sqrt{100} = 10cm \\ h = \frac{l \sqrt{3} }{2} = \frac{10 \sqrt{3} }{2} = 5 \sqrt{3} cm[/tex]
[tex]b)a = 3 \sqrt{3} {cm}^{2} \\ \frac{ {l}^{2} \sqrt{3} }{4} = 3 \sqrt{3} \\ {l}^{2} \sqrt{3} = 3 \sqrt{3} \times 4 \\ {l}^{2} \sqrt{3} = 12 \sqrt{3} \\ {l}^{2} = 12 \sqrt{3} \div \sqrt{3} \\ {l}^{2} = 12 \\ l = \sqrt{12} = \sqrt{4 \times 3} = 2 \sqrt{3} cm \\ h = \frac{l \sqrt{3} }{2} = \frac{2 \sqrt{3} \times \sqrt{3} }{2} = \frac{2 \times 3}{2} = 3cm[/tex]
[tex]c)a = \frac{49 \sqrt{3} }{2} {cm}^{2} \\ \frac{ {l}^{2} \sqrt{3} }{4} = \frac{49 \sqrt{3} }{2} \\ {l}^{2} \sqrt{3} \times 2 = 49 \sqrt{3} \times 4 \\ 2 {l}^{2} \sqrt{3} = 196 \sqrt{3} \\ {l}^{2} \sqrt{3} = 196 \sqrt{3} \div 2 \\ {l}^{2} \sqrt{3} = 98 \sqrt{3} \\ {l}^{2} = 98 \sqrt{3} \div \sqrt{3} \\ {l}^{2} = 98 \\ l = \sqrt{98} = \sqrt{49 \times 2} = 7 \sqrt{2} cm \\ h = \frac{l \sqrt{3} }{2} = \frac{7 \sqrt{2} \times \sqrt{3} }{2} = \frac{7 \sqrt{6} }{2} cm[/tex]
Pune A in loc de a la fiecare
