Question

The length of a rectangular field is twice its breadth if the perimeter of the field is 114 metres find the length and breadth of the field

Answer 1

Answer:

Given :

$\textsf{Length of the rectangular field is twice than breadth}$

$\textsf{Perimeter of the rectangular field = 114 m}$

To find :

$\textsf{Length and Breadth of the rectangular field}$

Concept :

Let the Length be 2x

And let the Breadth be x

So , now the formula to find the perimeter of the rectangular field is -:

$\large \sf\:\:\:\:\:\:\:\:\:\:\:\:\:{\boxed{\color{orange}{P=2(L+B)}}}$

Here ,

P = Perimeter

L = Length

B = Breadth

So , the equation by which the Length and Breadth we have to find like this :

$\large \sf\:\:\:\:\:\:\:\:\:\:\:\:\:{\boxed{\color{green}{2(2x+x)=114m}}}$

Solution :

$:\implies \sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{2(2x+x)=114m}$

Used cross multiplication

$:\implies \sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{4x+2x=114m}$

$:\implies \sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{6x=114m}$

$:\implies \sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x=\dfrac{114m}{6}}$

$:\implies \sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x=19m}$

So , the Breadth is 19 m .

To find the length do the twice of Breadth.

So ,

$\sf{Length = 19 m \times2}$

$\sf{Length=38m}$

So , the Length is 38 m .

Verification :

To verify the answer use the formula to find the perimeter of the rectangular field.

If the answer will come 114 m . Then the answer will be verified .

$:\implies \sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{2(L+B)}$

$:\implies \sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{2(19m+38m)}$

$:\implies \sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{2\times57m}$

$:\implies \sf\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{114m}$

Hence , the answer is verified .

Answer :

So ,

Breadth = 19 m

Length = 38 m

Answer 2

Step-by-step explanation:

Let,

Breadth= x

Length= 2x

According to the Question,

2× (2x+x)= 114

4x+2x= 114

6x= 114

x= 114÷6

= 19

So, Breadth=19m

Length= (19×2)m

= 38m