The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.
Let the shorter side of rectangular field be = x meter
The diagonal of the field = (x + 60) m
And, longer side is 30m more than shorter side = (x + 30) m
According to question;
Using Pythagoras theorem;
(x + 60)2 = x2 + (x + 30)2
x (x - 90) + 30 (x - 90) = 0
(x + 30) (x - 90) = 0
(x + 30) = 0 or (x - 90) = 0
Either, x = -30 or x = 90
But x ≠ -30 because length can never be negative.
Hence, shorter side of field is 90 m and longer side is (x + 30) = 120 m
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