Question

Calcule a medida de x e y na figura abaixo

Answer 1

Resposta:

${h}^{2} = mn \\ {b}^{2} = an \\ {c}^{2} = am \\ a = m + n \\ \\ {a}^{2} = {b}^{2} + {c}^{2}$

$(4 \sqrt{5} ) {}^{2} = {4}^{2} + {m}^{2} \\ \\ 16 \times 5 = 16 + {m}^{2} \\ \\ 80 - 16 = {m}^{2} \\ \\ 64 = {m }^{2} \\ \\ m = \sqrt{64} \\ \\ \pink{m = 8}$

${c}^{2} = am \\ \\ (4 \sqrt{5} ) {}^{2} = a(8) \\ \\ 80 = 8a \\ \\ a = \dfrac{80}{8} \\ \\ \pink{a = 10 }\\ \\ a = 8 + x \\ \\ 10 = 8 + x \\ \\ 10 - 8 = x \\ \\ \pink{x = 2}$

${y}^{2} = {4}^{2} + {2}^{2} \\ \\ {y}^{2} = 16 + 4 \\ \\ y = \sqrt{20} \\ \\ y = \sqrt{4 \times 5} \\ \\ y = \sqrt{4} \times \sqrt{5} \\ \\ \pink{y = 2 \sqrt{5} }$

Bons Estudos!