Dimensions 83603

The perimeter of the rectangle is 56 cm, and its length is three times greater than its width. What are the dimensions of the rectangle?

Correct answer:

a =  21 cm
b =  7 cm

Step-by-step explanation:

o=56 cm  o=2a+2b a=3b 56=2a+2b a=3b  56=2 a+2 b a=3 b  2a+2b=56 a3b=0  Row212 Row1Row2 2a+2b=56 4b=28  b=284=7 a=562b2=562 72=21  a=21 b=7o = 56 \ \text{cm} \ \\ \ \\ o = 2a+2b \ \\ a = 3b \ \\ 56 = 2a+2b \ \\ a = 3b \ \\ \ \\ 56 = 2 \cdot \ a+2 \cdot \ b \ \\ a = 3 \cdot \ b \ \\ \ \\ 2a+2b = 56 \ \\ a-3b = 0 \ \\ \ \\ Row 2 - \dfrac{ 1 }{ 2 } \cdot \ Row 1 → Row 2 \ \\ 2a+2b = 56 \ \\ -4b = -28 \ \\ \ \\ b = \dfrac{ -28 }{ -4 } = 7 \ \\ a = \dfrac{ 56-2b }{ 2 } = \dfrac{ 56-2 \cdot \ 7 }{ 2 } = 21 \ \\ \ \\ a = 21 \ \\ b = 7



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