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Question
The diagonal of a rectangle is 60 m more than its shorter side and the larger side is 30 m more than the shorter side. Find the sides of the rectangle.
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Solution
Let the shorter side be x m.
Length of the other side = (x + 30) m
Length of hypotenuse = (x + 60) m
Using Pythagoras theorem,
(x + 60)2 = x2 + (x + 30)2
x2 + 3600 + 120x = x2 + x2 + 900 + 60x
x2 – 60x – 2700 = 0
x2 – 90x + 30x – 2700 = 0
x(x – 90) + 30(x – 90) = 0
(x – 90)(x + 30) = 0
x = 90, –30
But, x cannot be negative.
So, x = 90.
Thus, the sides of the rectangle are 90 m and (90 + 30) m = 120 m.
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