-triângulo PQR-

Q

|\

|_\R

P

===============

1 dos catetos:

PQ = x + 3

outro cateto:

PR = x - 2

hipotenusa:

QR = x + 8

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a² = b² + a² = b² + c²

(x + 8)² = (x + 3)² + (x - 2)²

x² + 2.x.8 + 64 = x² + 2.x.3 + 9 + x² - 2.x.2 + 4

x² + 16x + 64 = x² + 6x + 9 + x² - 4x + 4

16x + 64 = x² + 2x + 13

14x + 51 = x²

x² - 14x - 51 = 0

x = -b +- /b² - 4ac

_________2a________

x = 14 +- /(-14)² - 4.1.(-51)

__________2__________________

x = 14 +- /196 + 204

__________2_________

x¹ = 14 + 20

________2___

x¹ = 34

_____2_

x¹ = 17

x² = 14 - 20

________2___

x² = -6

______2

x² = -3

===============

PQ = x + 3 -> 17 + 3 = 20

PR = x - 2 -> 17 - 2 = 15

QR = x + 8 -> 17 + 8 = 25

===============

p = 20 + 15 + 25

p = 60