Four pieces

A 37 cm board is cut into four pieces. The first and second pieces are equal in length, as are the third and fourth. The fourth piece is four times the difference between the length of the first piece and 10 cm. Find the length of the second piece.

Final Answer:

b =  11 cm

Step-by-step explanation:

$$\begin{gathered} a+b+c+d=37 \\ a=b \\ c=a \\ d=4\cdot (a-10) \\ a+b+c+d=37 \\ a-b=0 \\ a-c=0 \\ 4a-d=40 \\ Pivot:Row1\leftrightarrow Row4 \\ Row2-\frac{1}{4}\cdot Row1\to Row2 \\ -b+0.25d=-10 \\ Row3-\frac{1}{4}\cdot Row1\to Row3 \\ -c+0.25d=-10 \\ Row4-\frac{1}{4}\cdot Row1\to Row4 \\ b+c+1.25d=27 \\ Row4+Row2\to Row4 \\ c+1.5d=17 \\ Row4+Row3\to Row4 \\ 1.75d=7 \\ d=\frac{7}{1.75}=4 \\ c=\frac{-10-0.25d}{-1}=\frac{-10-0.25\cdot 4}{-1}=11 \\ b=\frac{-10-0.25d}{-1}=\frac{-10-0.25\cdot 4}{-1}=11=11\text{cm} \\ a=\frac{40+d}{4}=\frac{40+4}{4}=11 \\ a=11 \\ b=11 \\ c=11 \\ d=4 \end{gathered}$$

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