Question

Oblicz pole prostokąta A'B'C'D' podobnego do prostokąta ABCD w skali k=3, jeżeli |AB|=5cm, |BC|=8 cm.

Answer 1

1. Oblicz pole prostokąta A'B'C'D' podobnego do prostokąta ABCD w skali k = 3, jeżeli AB = 5 cm , BC = 8 cm
I sposób
PABCD = |AB|*|BC
PABCD = 5*8 = 40 cm²
PA'B'C'D' / PABCD = k²
PA'B'C'D' = k² * PABCD
PA'B'C'D' = 3² * 40 = 9 * 40 = 360 cm²

II sposób
|A'B' | = k*|AB|
|A'B'| = 3*5 = 15 cm
|B'C'| = k*|BC|
|B'C'| = 3*8 = 24 cm
PA'B'C'D' = |A'B'|*|B'C'|
PA'B'C'D' = 15 * 24 = 360 cm²

Answer 2

k = 3

IABI = 5cm,  IBCI = 8cm

P"/p = k^2 = 3^2

P"/P = 9

P" = ?

 

P"/P = 9

P" = 9P = 9 x 5cm x 8cm

P" = 360 cm2

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Odp.Pole prostokata A"B"C"D" wynosi 360cm2.

 

Lub;

IA"B"I = kIABI

IA"B"I = 3 x 5cm = 15cm

IB"C"I = kIBCI

IB"C"I = 3 x 8cm = 24cm

P" = 15cm x 24cm

P" = 360 cm2

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