Question

The area of a rectangular plot is $528m^2.$ The length of the plot (in metres) is one metre more than twice its breadth. Find the length and the breadth of the plot.

Answer 1

(i) Let the breadth of the rectangular plot = xm
Hence, the length of the plot is (2x+1)m.
Formula of area of rectangle = length×breadth=528m2
Putting the value of length and width, we get
(2x+1)×x=528
⇒2x2+x=528
⇒2x2+x−528=0
⇒2x2−32x+33x−528=0
⇒2x(x−16)+33(x−16)=0
⇒(2x+33)(x−16)=0
Either 2x+33=0orx−16=0
⇒x= $\frac{-33}{2}$orx=16
As the length and breadth cannot be in negative values,
x=16, breadth = 16m
Length =2×16+1
= 33m