Question

como resolver pelo teorema de pitagoras:
(3√5)² = x² + (x/2)²
passo a passo por favor

Answer 1

${(3 \sqrt{5} )}^{2} = {x}^{2} + {( \frac{x}{2} )}^{2} \\ {3}^{2} \times {( \sqrt{5} )}^{2} = {x}^{2} + \frac{ {x}^{2} }{ {2}^{2} } \\ 9 \times \sqrt{ {5}^{2} } = {x}^{2} + \frac{ {x}^{2} }{4} \\ 9 \times 5 = \frac{4 {x}^{2} }{4} + \frac{ {x}^{2} }{4} \\ 45 = \frac{4 {x}^{2} + {x}^{2} }{4} \\ 45 = \frac{5 {x}^{2} }{4} \\ 5{x}^{2} = 45 \times 4 \\ {x}^{2} = \frac{45 \times 4}{5} \\ {x}^{2} = 9 \times 4 \\ x = \sqrt{9 \times 4} \\ x = \sqrt{9} \times \sqrt{4} \\ x = 3 \times 2 \\ x = 6$