Question

The area of a rectangular plot is 528 m 2 . The length of the plot (in meters) is one more than twice its breadth. find the length and breadth of the plot.

Answer 1

Given:

Area of the rectangle = 528 m²

Now:

Let the breadth of the rectangle be 'x' m.

Length of the rectangle = (2x + 1) m

We know that:

$\boxed{\sf{Area\:of\:the\:rectangle = l \times b}}$

$\implies$ (2x + 1) × x = 528

$\implies$ 2x² + x - 528 = 0

$\implies$ 2x² + 33x - 32x - 528 = 0

By middle term splitting:

$\implies$ x(2x + 33) - 16(2x + 33) = 0

$\implies$ (x - 16) (2x + 33) = 0

$\implies$ (x - 16) or (2x + 33) = 0

We get:

$\boxed{\sf{x = 16\:or\:x =-\frac{33}{2}}}$

Since:

The breadth can't be negative, so x ≠ - 33/2

Therefore:

$\huge\boxed{\sf{x = 16}}$

Breadth of the rectangle = x =  16 m

Length of the rectangle:

$\implies$ 2x + 1

$\implies$ (2 × 16 + 1)

$\implies$ 32 + 1

$\implies$ 33 cm  

Hence:

The length and the breadth of the plot is 33 cm and 16 cm.

Answer 2

Answer:

Let breadth be x

Then length is (2x+1)

We know,

Area of rectangle = length × breadth

528 = (2x+1)(x)

2x² + x - 528 = 0 - - - - - - - - - (1)

Now you can solve this equation by any method but I am going to solve it by splitting the middle term,

2x² + 33x - 32x - 528 = 0

x(2x+33)-16(2x+33)=0

(x-16)(2x+33)=0

x-16=0 2x+33=0

x=16 x= - 33/2

As the second value is negative, we will neglect it.

So breadth=x=16

Length= (2x+1)=2(16)+1=33

Hope it helped you