the length of a rectangle exceeds its breadth by 5m.If the breadh were doubled and the length reduced by 9m,the area of rectangle would have have increased by 140m2 .Find its dimensions.

breadth=x

length=x+5

area=x*(x+5)=x2 +5x

breadth doubled=2x

length reduced by 9m= x+5-9=x-4

new area=2x*(x-4)=2x2 -8x

therefore

2x2 -8x=x2 +5x+140

x2 -13x-140=0

x2 -20x+7x-140=0

x(x-20)+7(x-20)=0

x=20 or -7

breadth=20

length=25

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A point X divides the line segment joining point P (4,-5) and Q(-3,8) such that PX/PQ=K/K+1.If X lies on the line x+y=0,then find the value of k and x.

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