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# 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. Q.6

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How i solve this question of class 10th of quadratic equation. It is very important type of question. 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.

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1. Let us say, the shorter side of the rectangle beÂ xÂ m.

Then, larger side of the rectangle = (xÂ + 30) m

As given, the length of the diagonal is = x + 30 m

Therefore,

â‡’Â x2Â + (xÂ + 30)2Â = (xÂ + 60)2

â‡’Â x2Â +Â x2Â + 900Â + 60xÂ =Â x2Â + 3600Â + 120x

â‡’Â x2Â â€“ 60xÂ â€“ 2700 = 0

â‡’Â x2Â â€“ 90xÂ + 30xÂ â€“ 2700 = 0

â‡’Â x(xÂ â€“ 90)Â + 30(xÂ -90) = 0

â‡’ (xÂ â€“ 90)(xÂ + 30) = 0

â‡’Â xÂ = 90, -30

However, side of the field cannot be negative. Therefore, the length of the shorter side will beÂ 90 m.

and the length of the larger side will be (90 + 30) m = 120 m.

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