Rectangle 3290

The rectangle 1 m and 40 cm long and 1 m and 20 cm wide is paved with square tiles with a side of 1 dm. There is one row of brown tiles on all edges of the rectangle, white on the inside. How many brown and how many white tiles?

Correct answer:

a =  48
b =  120

Step-by-step explanation:

$$\begin{gathered} x=1+40/100=\frac{7}{5}=1\frac{2}{5}=1.4\text{m} \\ y=1+20/100=\frac{6}{5}=1\frac{1}{5}=1.2\text{m} \\ s=1\text{dm}\to \text{m}=1:10\text{m}=0.1\text{m} \\ {S}_1=x\cdot y=1.4\cdot 1.2=\frac{42}{25}=1\frac{17}{25}=1.68{\text{m}}^2 \\ {S}_2=(x-2\cdot s)\cdot (y-2\cdot s)=(1.4-2\cdot 0.1)\cdot (1.2-2\cdot 0.1)=\frac{6}{5}=1\frac{1}{5}=1.2{\text{m}}^2 \\ {S}_3=s^2=0.1^2=\frac{1}{100}=0.01{\text{m}}^2 \\ a=(S_1-S_2)/S_3=(1.68-1.2)/0.01=48 \end{gathered}$$

$b=S_2/S_3=1.2/0.01=120$

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