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A rectangular plot has a concrete path running in the middle of the plot parallel to the breadth of the plot. The rest of the plot is used as a lawn, which has an area of 240m2. If the width of . the path is 3m and the length of the plot is greater than its breadth by 2m, what is the area of the rectangular plot?
(Geometry (Rectangle))Let us depict the rectangular plot according to question
Let, the width of the plot is x meter
∴Length of the plot is (x + 2) meter
According to question
3x + 240 = x(x + 2)
=3x+240=x²+2x
=x2-x-240=0
=x2 - 16x + 15x - 240 = 0
=x(x-16)+15(x-16)=0
=(x - 16)(x + 15) = 0
=Here r - 16 = 0
x = 16
x + 15 = 0
⇒x=-15 is not acceptable
Area of the plot = x(x+2)m² = 16(16+2)m² = 16 x 18=288m² (answer).
