Question

the area of rectangular plot 528 m² the length of plot is one more than twise its breadth we used to find length and breadth of plot​

Answer 1

Given :-

Area  of rectangular plot 528 m² the length of plot is one more than twise its breadth

To Find :-

Length and breadth

Solution :-

We know that

Area = Length × Breadth

Let the breadth be x

Length = 2x + 1

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

$\sf 2x^2 +x=528$

$\sf 2x^2+x-528 = 0$

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

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

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

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

Either

x - 16 = 0

x = 16

or

2x + 33 = 0

2x = 0 - 33

2x = -33

x = -33/2

Breadth can't be negative.

So, x = 16 m

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

Answer 2

Given,

• The Area of rectangular plot = 528m².
• The Length of plot is one more than twice its breadth i.e., Length = 2(breadth) + 1.

To Find,

• Length of Rectangular plot = ?
• Breadth of Rectangular plot = ?

Solution :

$\longrightarrow$Suppose the breadth of Rectangular plot be "b"

And, Length of Rectangular plot be "l"

∴According to First Condition :

• Area of Rectangular plot = 528m²

So, We know that:-

→Area of Rectangle = Length × Breadth

∴ l × b = 528 ...1)

Now,

According to Second Condition :

• The Length of plot is one more than twice its breadth

∴ Length = 2b + 1

Therefore,

Put the Value of Length in 1) Equation :-

∴ (2b + 1) × b = 528

→2b² + b = 528

→2b² + b - 528 = 0

Now, Find the value of b with the help of factorisation :-

∴2b² -32b + 33b - 528 = 0

→2b(b - 16) + 33(b - 16) = 0

→(b - 16) (2b + 33)

Either,

→b - 16 = 0

→b = 16

Or,

→2b + 33 = 0

→2b = -33

→b = -33/2

So, Value of breadth cannot be negative

Therefore,

Breadth = 16(Answer)

And, Length = 2b + 1

→Length = 2(16) + 1

→Length = 32 + 1

Length = 33 (Answer)