Question

The area of a rectangular plot is 528 m2. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.​

Answer 1

AnswEr:

Let us Consider that the Breadth of the Rectangular plot be x m.

Then, Length of the plot = (2x + 1)m

We know that,

$\small{\underline{\boxed{\sf{\red{Area\:of\: Rectangle\:=\: Length \times\: Breadth}}}}}$

Area of Rectangle = 528m² [Given]

Now,

$:\implies\sf\: (2x \:+\:1)x = 528$

$:\implies\sf\:2x^2 \: +\: x \:=\; 528$

$:\implies\sf 2x^2 \:+\: x \:-\;528 = 0$

Now, Solving Quadratic Equation

$:\implies\sf\:2x^2 +( 33x - 32)x - 528 = 0$

$:\implies\sf\:2x^2 + 33x - 32x - 528 = 0$

$:\implies\sf\:x(2x \: +\;33) \:- 16 (2x\:+\:33)$

$:\implies\sf\: (x \:-\:16) \; or \; (2x \:+\:33)$

$:\implies\sf\: x - 16 = 0$

$:\implies\large\boxed{\sf{\pink{x\:=\;16}}}$

$:\implies\sf\:2x + 33$

$:\implies\large\boxed{\sf{\pink{x\:=\:\dfrac{- 33}{\:\:2}}}}$

Finding Length & Breadth of the Rectangular plot :-

$:\implies\sf\: Length \:=\; (2x\;+\:1)m$

$:\implies\sf\: Length \:=\: (2\times\: 16 \: +\:1)$

$:\implies\sf\: Length \:=\; 32 \: + \: 1$

$:\implies\large\boxed{\sf{\pink{Length \:=\: 33\:m }}}$

$:\implies\large\boxed{\sf{\pink{Breadth\:=\;16\;m}}}$

Hence, Length & Breadth of the Rectangular plot is 33 m & 16m.

Answer 2

Question: The area of a rectangular plot is $528^{2}$. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.​

Given: Area of a rectangular plot $=528^{2}$

Length of the plot $=(2x=1)m$

To Find: The length and breadth of the plot.

Solution: Let the breadth of the rectangular plot $=x\:m$

Hence, the length of the plot is $(2x+1)m.$

Formula of area of rectangle $=length\times breadth= 528m^{2}$

Putting the value of length and width, we get,

$(2x+1) \times x = 528$

$:\implies$ $\boxed {2x^{2}+x=528 }}$

$:\implies$ $\boxed{2x^{2}+x-528=0}$

Solve the quadratic equation,

$2x^{2} +(33x-32) \times -528=0$

$x(2x+33)-16(2x+33)$

$x-16$

$x-16=0$

$:\implies \boxed{x=16}$

$2x+33$

$x= \frac{-33}{2}$

Length = $2 \times 16+1$

$\boxed{ Length=33m.}$

$\boxed{Breadth=16m.}$