The diagonal of a rectangular field is 60, m | vedclass

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(C) Let the shorter side of the rectangle be $x\, m$.Then,the longer side of the rectangle is $(x+30)\, m$.According to the Pythagorean theorem,the di

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$120$

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(C) Let the shorter side of the rectangle be $x\, m$.Then,the longer side of the rectangle is $(x+30)\, m$.According to the Pythagorean theorem,the diagonal of the rectangle is $\sqrt{x^2 + (x+30)^2}$.It is given that the diagonal is $60\, m$ more than the shorter side,so $\sqrt{x^2 + (x+30)^2} = x + 60$.Squaring both sides,we get $x^2 + (x+30)^2 = (x+60)^2$.Expanding the terms: $x^2 + x^2 + 60x + 900 = x^2 + 120x + 3600$.Simplifying the equation: $x^2 - 60x - 2700 = 0$.Factoring the quadratic equation: $x^2 - 90x + 30x - 2700 = 0$,which gives $x(x-90) + 30(x-90) = 0$.So,$(x-90)(x+30) = 0$.This gives $x = 90$ or $x = -30$.Since the length cannot be negative,the shorter side is $90\, m$.The longer side is $x + 30 = 90 + 30 = 120\, m$.

The diagonal of a rectangular field is $60\, m$ more than the shorter side. If the longer side is $30\, m$ more than the shorter side,find the sides of the field. (in $m$)

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