Question

the length of the rectangular field is 8 more than twice its breadth the distance around a rectangular field is 400 metres calculate the length and breadth of the field​

Answer 1

Answer:

#Given:

$Length\:more\:than\:breadth$

$=8\:more\:than\:twice\:its\:breadth$

$Distance\:around\:the\:rectangular\:field$

$=400\:m$

#To find:

$(i)Length\:of\:the\:rectangular\:field$

$(ii)Breadth\:of\:the\:rectangular\:field$

#Taken:

A/Q the equation which will be form to find the breadth will be :

$B=2x+8=400$

Where,

B = Breadth of the 2 side of the rectangular field

(400 m is the perimeter or the distance of the rectangular field)

#Concept:

$\textsf{After finding the breadth then find the length}$$\textsf{by using this equation}$

$L=P-B$

Where,

L = Length of the two sides of the rectangular field

P = Perimeter of the rectangular field

B = Breadth of the both side of the rectangular field

#Solution:

Breadth:

$\bold\purple{Taken,2x+8=400}$

$\Rightarrow{2x+8=400}$

$\Rightarrow{2x=400-8}$

$\Rightarrow{2x=392}$

$\Rightarrow{x=392/2}$

$\Rightarrow{x=196m}$

So , we have find the breadth of both side of the rectangular field.

So , to find the breadth of one side use this equation:

$Taken,B1=B/2$

Where,

B1 = Breadth of one side of the rectangular field

B = Breadth of two sides of the rectangular field

Breadth of one side :

$B1=B/2$

$B1=196/2$

$B1=98m$

____________________________________

Length:

$\bold\purple{Taken,L=P-B}$

$\Rightarrow{L=P-B}$

$\Rightarrow{L=400m-196m}$

$\Rightarrow{L=204m}$

So , we have find the length of the two sides of the rectangular field

Now , find the length of one side of the rectangular field by using the same equationas we have finded in the breadth of one side :

$Taken,L1=L/2$

Where,

L1 = Length of one side of the rectangular field

L = Length of the two sides of the rectangular field

Length of one side:

$L1=L/2$

$L1=204m/2$

$L1=102m$

#Answer:

(i) Length of the rectangular field:

2 sides = 204 m

1 side = 102 m

(ii) Breadth of the rectangular field

2 sides = 196 m

1 side = 98 m

#Verification:

To verify use the formula to find the perimeter of the rectangle:

Equation:

$P=2×(L1+B1)$

Where,

P = Perimeter of the rectangular field

L1 = Length of the rectangular field of one side

B1 = Breadth of the rectangular field of one side

Now , find the perimeter of the rectangular field for verification:

$P=2×(L+B)$

$P=2×(102m+98m)$

$P=2×200m$

$P=400m$

$\huge\color{red}{\fbox{Hence,Verified}}$

#Addional information:

To find the area of the rectangle:

$AR=L×B$

Where,

AR = Area of the rectangle

L = Length of the rectangle

B = Breadth of the rectangle

To find the area of the triangle:

$AT=\frac{H×B}{2}$

Where,

AT = Area of the triangle

H = Height of the triangle

B = Breadth of the triangle

$\huge\color{green}{\fbox{\underline{\dag{Be\:Brainly}}}}$

Answer 2

» To Find :

The Length and Breadth of the Rectangular field.

» Given :

Let the Breadth be x.

So , According to the question , Length is 8 more than the twice of Breadth.

So the equation formed is :

$\sf{\underline{\boxed{l = 8 + 2x}}}$

Hence ,

• Length = 8 + 2x

• Breadth = x

• Perimeter = 400 m

» We Know :

Perimeter of a rectangle :

$\sf{\underline{\boxed{P_{r} = 2(l + b)}}}$

Where ,

• P = Perimeter of the Rectangle

• l = Length of the Rectangle

• b = Breadth of the Rectangle

» Concept :

According to the question , it is given that the distance around the Rectangular field is given ,so we can take it as the perimeter of the Rectangle.

And to find the length and breadth of the Rectangle ,we have to first find the value of x.

» Solution :

Given :

• Length = 8 + 2x

• Breadth = x

• Perimeter = 400 m

Formula :

$\sf{\underline{\boxed{P_{r} = 2(l + b)}}}$

Substituting the values in it ,we get :

$\sf{\Rightarrow 400 = 2((8 + 2x) + x)}$

$\sf{\Rightarrow 400 = 2(8 + 3x)}$

$\sf{\Rightarrow 400 = 16 + 6x}$

$\sf{\Rightarrow 400 - 16 = 6x}$

$\sf{\Rightarrow 384 = 6x}$

$\sf{\Rightarrow \dfrac{384}{6} = x}$

$\sf{\Rightarrow \cancel{\dfrac{384}{6}} = x}$

$\sf{\Rightarrow 64 = x}$

Hence ,the value of x is 64 m.

Now , putting the value of x in the length and breadth ,we get :

• Breadth ➝ x = 64 m
• Length ➝ 8 + 2x

➝ 8 + 2 × 64

➝ 8 + 128

➝ 136 m

Hence , the length is 136 m and breadth is 64 m.

» Additional information :

• Area of a rectangle = length × Breadth

• Area of a square = (side)²

• Surface area of a Cube = 6(a)²

• Curved surface area of a Cube = 4(a)²