# Two rectangles 2

A square of area 36 cm2 is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.

Result

a =  4 cm
b =  6 cm
c =  2 cm
d =  6 cm

#### Solution:

$S = 36 \ cm^2 \ \\ S = x^2 \ \\ \ \\ x = \sqrt{ S } = \sqrt{ 36 } = 6 \ cm \ \\ \ \\ S_{ 1 } = \dfrac{ 2 }{ 2+1 } \cdot \ S = \dfrac{ 2 }{ 2+1 } \cdot \ 36 = 24 \ cm^2 \ \\ S_{ 2 } = \dfrac{ 1 }{ 2+1 } \cdot \ S = \dfrac{ 1 }{ 2+1 } \cdot \ 36 = 12 \ cm^2 \ \\ \ \\ a = S_{ 1 }/x = 24/6 = 4 = 4 \ \text { cm }$
$b = x = 6 = 6 \ \text { cm }$
$c = S_{ 2 }/x = 12/6 = 2 = 2 \ \text { cm }$
$d = x = 6 = 6 \ \text { cm }$

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