Two rectangles 2

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

Final Answer:

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

Step-by-step explanation:

$$\begin{gathered} S=36{\text{cm}}^2 \\ S=x^2 \\ x=\sqrt{S}=\sqrt{36}=6\text{cm} \\ {S}_1+S_2=S \\ {S}_1:S_2=2:1 \\ {S}_1=\frac{2}{2+1}\cdot S=\frac{2}{2+1}\cdot 36=24{\text{cm}}^2 \\ {S}_2=\frac{1}{2+1}\cdot S=\frac{1}{2+1}\cdot 36=12{\text{cm}}^2 \\ {S}_1=a\cdot x \\ {S}_2=c\cdot x \\ a=S_1/x=24/6=4\text{cm} \end{gathered}$$

$b=x=6=6\text{cm}$

$c=S_2/x=12/6=2\text{cm}$

$d=x=6=6\text{cm}$

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