Question

calcule o valor de ×nos triângulos retangulos

Answer 1

a) $x^{2} + (3 \sqrt{3})^{2} = (2x)^{2} \\ x^{2} + 9*3 = 2^{2}*x^{2} \\ x^{2} + 27 = 4x^{2} \\ 3x^{2} = 27 \\ x^{2} = 9 \\ x = 3$

b) $(x + 3)^{2} + 6^{2} = (x + 5)^{2} \\ x^{2} + 6x + 9 + 36 = x^{2} + 10x + 25 \\ 4x = 20 \\ x = 5$

Answer 2

a
a(  hipotenusa )  = 2x
b  cateto  =  x
c  cateto = 3V3
aplicando Pitágoras  a² = b² + c²
(2x)²  = ( 3V3)²  + (x)²
4x² = 3² . 3  + x²
4x² = 9 .3 + x²
4x² = 27 + x²
4x²-x²  = 27
3x² = 27
x² = 27/3=9
x² = 9
Vx² = V9
x = 3 ***

b
a ( hipotenusa ) = ( x + 5 )
b = cateto  = ( x + 3 )
c = cateto   =  6
( x + 5)²  = ( x + 3)²  + 6² 
[ (x)²  + 2 * x * 5  + (5)²]  =  [ (x)² + 2 * x * 3 + ( 3)²]  + 36
( x² + 10x + 25 ) = ( x² + 6x + 9 ) + 36
x² - x² + 10x - 6x + 25 - 9 - 36 = 0
4x - 20  =0
4x = 20
x = 20/4 = 5 ****