Respuesta :

Answer:

a=10

Step-by-step explanation:

Using Pythagoras theorem

[tex] {(a + 2)}^{2} + {( a- 5)}^{2} = {(a + 3)}^{2} [/tex]

[tex] {a}^{2} + 4a + 4 + {a}^{2} - 10a + 25 = {a}^{2} + 6a + 9[/tex]

simplify:

[tex] {a}^{2} - 12a + 20 = 0[/tex]

(a-2)(a-10)=0

hence a= 2 or a=10 however we must reject 2 as the lengths of the triangle cannot be negative eg. the side for a-5 will be equivalent to -3 cm which is not possible for lengths to become negative