Respuesta :

Answer:

a=10

Step-by-step explanation:

use a^2+b^2=c^2

(a+2)^2+(a-5)^2=(a+3)^2

a^2+4a+4+a^2-10a+25=a^2+6a+9

2a^2-6a+29=a^2+6a+9

a^2-12a=-20

a^2-12a+20=0

quadratic formula→(12+/-8)/2

a=10 or 2

2 is not an option because 2-5=-3 which isn't possible in this case.

so a=10

Apply Pythagorean theorem

  • (a-5)²+(a+2)²=(a+3)²
  • a²-10a+25+a²+4a+4=a²+6a+9
  • a²-6a+29=6a+9
  • a²-12a+20=0
  • a²-10a-2a+20=0
  • a(a-10)-2(a-10)=0
  • (a-2)(a-10)=0
  • a=2,10

There is a side a-5 so 2 is not a answer

  • a=10

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