Question

Area of rectangular plot is 2112m².the length of plot is 2m more 2 times the breadth.Find the perimeter of plot​

Answer 1

Given :

• Area of rectangular plot is 2112 m².

• Length of plot is 2m more 2 times the breadth.

To find :

• The perimeter of Plot =?

Step-by-step explanation :

Let, the breadth of the rectangular plot be, x.

Then, the length of the rectangular plot be, 2x

And , it is also given that,

Length of plot is 2m more 2 times the breadth.So,

Length of rectangular plot = 2 + 2x

Area of rectangular plot is 2112 m². [Given]

As We know that,

Area of Rectangle = length x breadth.

Substituting the values in the above formula, we get,

➟ 2112 = x × (2 + 2x)

➟ 2112 = 2x + 2x²

➟ 2x + 2x² = 2112

➟ 2x + 2x² - 2112 = 0

➟ 2x² +2x - 2112 = 0

➟ x + x² - 1056 = 0

➟ x² + x - 1056 = 0

➟ x² + 33x - 32x - 1056 = 0

➟ x(x + 33) - 32(x + 33) = 0

➟ (x+33) (x - 32) = 0

So,

x = -33 [Ignor negative]

Or x = 32

Therefore, We got the value of, x = 32.

Hence,

Breadth of the rectangular plot,x = 32 m.

Length of the rectangular plot,

= 2 + 2x

= 2 + 2 × 32

= 2 + 64

= 66

Length of the rectangular plot = 66 m

Now,

Perimeter of the rectangular plot = Perimeter of rectangle = 2 ( length + breadth)

Substituting the values in the above formula, we get,

= 2 (66 + 32)

= 2 (98)

= 196.

Therefore, Perimeter of the rectangular plot = 196 m.

Answer 2

Given:-

• Area of rectangular plot = 2112m²

• Length of plot is 2m more 2times the breadth.

To Find:-

• Perimeter of plot

Solution :-

According to the Question

Let, the breadth of rectangular plot = b

and ,

length is 2 m more 2 time breadth= 2b + 2

We know that

,Area of rectangle = l × b

where

l is the length of rectangle .

b is the breadth of rectangle.

➦ Area of rectangle = 2112m²

➭ l × b = 2112

putting the values of l and b

➭ (2b + 2) × b = 2112

➭ 2b²+ 2b = 2112

➭ 2b² +2b - 2112= 0

dividing both side from 2

➭ b² +b -1056=0

➭ b²+ 33b -32b -1056=0

➭ b ( b +33) - 32b - 1056 = 0

➭ b ( b+33) -32 (b - 32) = 0

When the product of factors equal 0 then at least one factor is 0.

here

b + 33 =0 b = -33

b -32=0 b = 32

b1 = -33 and b2 = 32

breadth cannot be negative

∴ The breadth of the rectangular plot is 32m

and length = 2×32+2= 66m

Now, we know that perimeter of rectangle = 2(l+b)

➦ Perimeter of rectangular plot = 2(l+b)

➭ Perimeter of rectangular plot =2 ( 66+32)

➭ Perimeter of rectangular plot = 196m

∴ The perimeter of rectangular plot is 196m