Question

Halle el área y perímetro del triangulo mostrado. Las dimensiones están em metros

Answer 1

Explicación paso a paso:

$( {x + 3)}^{2} + ( {x - 4)}^{2} = ( {2x - 5)}^{2} \\ {x }^{2} + 6x + 9 + {x}^{2} - 8x + 16 = 4 {x}^{2} - 20x + 25 \\ 2 {x }^{2} - 2x + 25 = 4 {x}^{2} - 20x + 25 \\ 2 {x}^{2} - 2x + 25 - 4 {x}^{2} + 20x - 25 = 0 \\ - 2 {x}^{2} + 18x = 0 \\ 18x = 0 + 2 {x}^{2} \\ 18x = 2 {x}^{2} \\ 18 = 2x \\ x = \frac{18}{2} = 9 \\ x = 9$

Base=x-4=9-4=5

Altura=x+3=9+3=12

Hipotenusa=2x-5=2(9)-5=18-5=13

Perimetro=a+b+c=5+12+13=30

Area=bh/2=5x12/2=60/2=30