Question

the lenth of a rectangular filed is 8m less than twice breadth . if the perimeter of rectangular filed is 56 meters, find is length and breadth?​

Answer 1

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It is said that the length of a rectangular field is 8m less than twice breadth and the perimeter of rectangular filed is 56 meters. Now, first we will consider it's length and breadth be in terms of variable. Thereafter , we will have our length and breadth respectively.

Let we consider the breadth be " x " metre.

Then, the Length → 2x - 8

Because length of a rectangular field is 8m less than twice breadth.

Formula need to know :

It is said that the length of a rectangular field is 8m less than twice breadth and the perimeter of rectangular filed is 56 meters. Now, first we will consider it's length and breadth be in terms of variable. Thereafter , we will have our length and breadth respectively.

Let we consider the breadth be " x " metre.

Then, the Length → 2x - 8

Because length of a rectangular field is 8m less than twice breadth.

Formula need to know :

$\begin{gathered}{\boxed{\sf{Perimeter \: of \: the \: rectangle = 2 ( l + b ) }}} \\ \\ \end{gathered}$

The length of a rectangular field is 8m less than twice it's breadth.if the perimeter of the rectangular field is 56 meters.

Substituting the respective values :

Perimeter of rectangle → 56 m

Length → 2x - 8 metres

Breadth → " x " metres

$\begin{gathered}\dashrightarrow\:\:\sf 2(length + breadth) = 56 \\ \\ \end{gathered}$

$\begin{gathered}\dashrightarrow\:\:\sf 2[(2x - 8) + x] = 56\\ \\ \end{gathered}$

$\begin{gathered}\dashrightarrow\:\:\sf 2x - 8 + x = \dfrac{56}{2} \\ \\ \end{gathered}</p><p>$

$\begin{gathered}\dashrightarrow\:\:\sf 3x = 36 \\ \\ \end{gathered}$

$\begin{gathered} \sf \longrightarrow \: x \: = {\dfrac{ \cancel{36}^{ \: \: 12} }{ \cancel{3}^{ \: \: 1} } \: m} \\ \\ \end{gathered}$

$\begin{gathered}\dashrightarrow\:\:\sf x = 12 \\ \\ \end{gathered}$

Hence,

$\begin{gathered}\dashrightarrow\:\: \underline{ \boxed{\sf Breadth \: of \: Rectangle = 12 \: m}} \\ \\\end{gathered}$

BreadthofRectangle=12m

And now we know ,

Length of rectangle = (2x - 8)

(2 × 12 ) - 8

24 - 8

16

$\begin{gathered}\dashrightarrow\:\: \underline{ \boxed{\sf Breadth \: of \: Rectangle = 12 \: m}} \\ \\\end{gathered}$

Answer 2

Let length and breadth the field are l and b respectively. Then,

l=2b−8⇒2b=8+l⟶(1)

The perimeter of the rectangular field =56 m

⇒2(l+b)=56m⇒2l+2b=56m

from (1), we get

2l+8+l=56⇒3l=48⇒l=16m

∴ Length of rectangular field =16m

Breadth of rectangular field

$= \frac{16 + 8}{2}$