SOLUTION: two rectangular plots are of equal area. the length of the first plot is one and a half times its width. the length of the second plot is 7 meter less than three times its width.

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Question 857702: two rectangular plots are of equal area. the length of the first plot is one and a half times its width. the length of the second plot is 7 meter less than three times its width.
a) denoting the width of the first plot by x meters and the the width of the second plot by y meters, derive a relation between x and y
b)if y=x+1 calculate the value of x only
Answer by mananth(16946) (Show Source):
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two rectangular plots are of equal area. the length of the first plot is one and a half times its width. the length of the second plot is 7 meter less than three times its width.

width of first plot = x
length of first plot = 1.5x

width of second plot = y
length of second plot =3y-7
(3/2)x^2 = y(3y-7)
x^2= (2y/3)(3y-7)
x^2= (2(x+1)/3) (3(x+1)-7)

x^2= (2x+2)/3 (3x-4)
3x^2= (2x+2)(3x-4)
3x^2=6x^2-8x+6x-8
3x^2-2x-8=0
3x^2-6x+4x-8=0
3x(x-2)+4(x-2)=0
(x-2)(3x+4)=0
x=2 the positive value