Odpowiedź:
1.
O = 46 O = 2 x a + 2 x b
2a + 2b = 46/:2
a + b = 23
a = 23
b = ?
d = a + 2
d = (23 - b + 2) = (25 - b)
a2 + b2 = d2
(23 - b)2 + b2 = (25-b)2
529 - 46b + b2 + b2 = 625 - 50b + b2
2b2 - 46b + 50b - b2 - 625 + 529 = 0
b2 + 4b - 96 = 0
delta = 16 - 4 x 1 x (-96)
delta = 16 + 384
delta = 400
pierwiastek z delty = 20
b1 = -4 + 20/ 2 = 16/2 = 8
b2 = -4 - 20/2 = -24/2 = -12
b = -12
a = 24 - (-12)
a = 36
2.
O = 62cm O = 2 x a + 2 x b
2a + 2b = 62/:2
a + b = 31
a = 31
b = ?
d = a + 1
d = (31 - b + 1) = (32 - b)
a2 + b2 = d2
(31 - b)2 + b2 = (32-b)2
961 - 62b + b2 + b2 = 1024 - 64b + b2
2b2 - 62b + 64b - b2 - 1024 + 961 = 0
b2 + 2b - 63 = 0
delta = 4 - 4 x 1 x (-63)
delta = 256
delta = 256
pierwiastek z delty = 16
b1 = -2 + 16/ 2 = 7
b2 = -2 - 16/2 = - 9
b = -9
a = 31 - (-9)
a = 40
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