Four pieces

A 37-centimeter board is cut into four pieces. The first piece and the second piece are the same lengths. Similarly, the third and the fourth piece are the same lengths if the fourth piece is quadruple the difference between the first piece and 10 cm. Find the length of the second piece.

Correct answer:

b =  11 cm

Step-by-step explanation:

a+b+c+d=37 a=b c=a d=4⋅ (a−10)  a+b+c+d=37 a−b=0 a−c=0 4a−d=40  Pivot:Row1↔Row4 4a−d=40 a−b=0 a−c=0 a+b+c+d=37  Row2−41​⋅ Row1→Row2 4a−d=40 −b+0.25d=−10 a−c=0 a+b+c+d=37  Row3−41​⋅ Row1→Row3 4a−d=40 −b+0.25d=−10 −c+0.25d=−10 a+b+c+d=37  Row4−41​⋅ Row1→Row4 4a−d=40 −b+0.25d=−10 −c+0.25d=−10 b+c+1.25d=27  Row4+Row2→Row4 4a−d=40 −b+0.25d=−10 −c+0.25d=−10 c+1.5d=17  Row4+Row3→Row4 4a−d=40 −b+0.25d=−10 −c+0.25d=−10 1.75d=7  d=1.757​=4 c=−1−10−0.25d​=−1−10−0.25⋅ 4​=11 b=−1−10−0.25d​=−1−10−0.25⋅ 4​=11=11 cm a=440+d​=440+4​=11  a=11 b=11 c=11 d=4

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