Question

calcule o valor de x nos triângulos retângulos

Answer 1

$a) {(2x)}^{2} = {(3 \sqrt{3} })^{2} + {x}^{2} \\ 4 {x}^{2} = 9.(3) + {x}^{2} \\ 4 {x}^{2} - {x}^{2} = 27 \\ 3 {x}^{2} = 27 \\ {x}^{2} = \frac{27}{3} \\ {x}^{2} = 9 \\ x = \sqrt{9} \\ x = 3 \\ \\ b) {(x + 5)}^{2} = {(x + 3)}^{2} + {6}^{2} \\ {x}^{2} + 10x + 25 = {x}^{2} + 6x + 9 + 36 \\ {x}^{2} - {x}^{2} + 10x - 6x = 25 - 9 \\ 4x = 16 \\ x = \frac{16}{4} \\ x = 4$