A farmer has a field in the shape of a right angled triangle with perpendicular sides of lengths 128 m and 64 m. He wants to leave a space in the form of a square of largest size inside the field for growing wheat and remaining for growing vegetables. Find the length of the sides of such a square space .
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take triangle ABC with angle A as 90
inscribe a square in it. Name it as AEFD. Take its side as x.
therefore EB will be 128-x.
similarly DC will be 64-x.
Prove triangle BEF and FDC similar by AA test.
BE/FD=EF/DC
128-x/x=x/64
thus x=42.666667
therefore side will be 42.66
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