Question

Aplicando o teorema de Pitágoras, determine a medida x indicada em cada um dos triângulos retângulos

Answer 1

1 - a) 13

x² = 12² + 5²

x² = 144 + 25

x = $\sqrt{169}$

x = 13

b) $\sqrt{13}$

x² = 3² + 2²

x² = 9 + 4

x =      $\sqrt{13}$

c) $3\sqrt{2}$

x² = $(\sqrt{10})^{2}$ + $(2\sqrt{2})^{2}$

x² = 10 + 8

x =      $\sqrt{18}$

x =    $3\sqrt{2}$

d)    $3\sqrt{2}$

6² = x² + x²

36 = 2x²

18 = x²  

       $\sqrt{18}$ = x

 $3\sqrt{2}$ = x

e) 6

(x + 9)² = (x + 3)² + (2x)²

x² + 2x * 9 + 9² = x² + 2x * 3 + 3² + 4x²

x² + 18x + 81 = x² + 6x + 9 + 4x²

18x + 81 = 6x + 9 + 4x²

18x + 81 - 6x - 9 - 4x² - 0

12x + 72 - 4x² = 0

x² - 3 - 18 = 0

x = - (-3) ±√(-3)² - 4 * 1 * (-18) / 2 * 1

x = 3 ±√(-3)² - 4 * (-18) / 2

x = 3 ±√9 - 4 * (-18) / 2

x = 3 ±√9 + 72 / 2

x = 3 ±√81 / 2

x = 3 ± 9 / 2

x = $\frac{3 + 9}{2}$

x =  $\frac{12}{2}$

 x = 6

f) 3

$(\sqrt{26})^{2}$ =  $(\sqrt{17})^{2}$ + x²

26 = 17 + x²

26 - 17 = x²

     $\sqrt{9}$ = x

3 = x

2) Sim, pois:

26² = 24² + 10²

676 = 576 + 100

676 = 676

3) 11cm

14² = $(5\sqrt{3})^{2}$ + x²

196 = 75 + x²

196 - 75 = x²

$\sqrt{121}$ = x

11 = x

4) 5m

x² = 4² + 3²

x² = 16 + 9

x = $\sqrt{25}$

x = 5