Wire split and minimum combined area

Wire split and minimum combined area

Secondary 2
TGM Original Questions

An \(80\) m wire is split. One part forms a rectangle \(6x\) m by \(2x\) m; the remainder forms a square.

  1. Show the total area is \(A=28x^2-160x+400\).
    1. complete the missing table values \(a,b\)
    2. plot for \(1\le x\le4.5\)
    3. estimate the \(x\) giving minimum area.
\(x\)\(1\)\(1.5\)\(2\)\(2.5\)\(3\)\(3.5\)\(4\)\(4.5\)
\(A\)\(268\)\(223\)\(192\)\(a\)\(172\)\(183\)\(b\)\(247\)

Solution:

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Answer:(b)(i) \(a=175,b=208\); (iii) \(x\approx2.86\) m; minimum area \(\approx171.43\text{ m}^2\).

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