Obwd prostokata wznosi 32 cm. jezeli jeden bok zwiekszymy o 2 cm a drugi o 3 cm to pole powstalego prostokata zwiekszy sie o 47 cm kwadratowych. oblicz dlugosci bokow kazdego z prostokatow.
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Ob = 32cm
P = a * b
2a + 2b = 32
a * b = (a + 2) * (b + 3) - 47
a + b = 16
ab = ab + 3a + 2b - 47
a + b = 16
-3a - 2b = -47
2a +2b = 32
-3a - 2b = -47
----------------------
-a = -15
a = 15
a +b = 16
b = 16 - a
b = 16 - 15
b =1
odp. a = 15cm b = 1cm
Obw. = 32 cm
2(a + b) = 32 /:2
a·b = (a + 2)(b + 3) - 47
a + b = 16
ab = ab + 3a + 2b - 47
a + b = 16 I*(-2)
3a + 2b = 47
-2a - 2b = -32
3a + 2b = 47
------------------
a = 15 cm
b = 16 - 15
b = 1 cm
Odp. a = 15cm, b = 1 cm.