Q. 64.2( 236 Votes )
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.
To find: length and breadth of the field
Let the shorter side of the rectangle be x m.
Then, larger side of the rectangle = (x + 30) mwe know,
By pythagoras theorem,
(Hypotenuse)2 = (Base)2 + (Perpendicular)2
Diagonal of a rectangle is √[(length)2 + (breadth)2]
Diagonal of the rectangle =
It is given that the diagonal of the rectangle is 60 m more than the shorter side.
∴ = x+60Squaring both sides, we get,
⇒ x2 + (x+30)2 = (x+60)2
⇒ x2 +x2 +900+60x = x2+3600+120x
⇒ x2 – 60x – 2700 = 0Now for solving this quadratic equation, we need to factorize 60 in such a way that the product is 2700 and the difference is 60
⇒ x(x – 90 )+30(x – 90 ) = 0
⇒ (x - 90)(x+30) = 0
⇒ x = 90, -30
However, side cannot be negative. Therefore, the length of the shorter side will be 90 m.
Hence, length of the larger side will be (90 + 30) m = 120 m
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