Question

The perimeter of a rectangular field is 56 metres. its length is 8 metres less than twice its breadth. what are the length and the breadth of the field.​

Answer 1

★Given : The perimeter of a rectangular field is 56 metres. its length is 8 metres less than twice its breadth.

$\rule{130}1$

★Solution :

Let the Breadth be x.

Then, Length = 2x - 8

$\rule{130}1$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

★ Perimeter = 2 ( Length + Breadth )

→ 56 = 2 (x + 2x - 8)

→ 56/2 = 3x - 8

→ 28 = 3x - 8

→ 3x = 28 - 8

→ 3x = 36

→ x = 36/3

→ x = 12 m

$\therefore\:\underline{\textsf{The Breadth of the reactangular field is \textbf{12 m}}}.$

$\rule{130}1$

Now,

→ Length = 2x - 8

→ Length = 2(12) - 8

→ Length = 36 - 8

→ Length = 16 m

$\therefore\:\underline{\textsf{The length of the reactangular field is \textbf{16 m}}}.$

$\rule{170}2$

Answer 2

ANSWER✔

$\large\underline\bold{GIVEN,}$

$\sf\dashrightarrow perimeter\:of\:rectangle \:field\:is\:56\:meters$

$\sf\dashrightarrow length\:is\: twice\:than\:breadth\:and\:8m\:less\:than \:breadth$

$\large\underline\bold{TO\:FIND,}$

$\sf\dashrightarrow LENGTH\:AND\:BREADTH\:OF\:RECTANGLE.$

✯FORMULA IN USE,

PERIMETER OF RECTANGLE=2×(L+B)

ACCORDING TO THE QUESTION,

$\sf\dashrightarrow BREADTH\:BE\:"X"$

$\sf\therefore LENGTH\:WILL\:BE\:2x-8$

$\large\underline\bold{SOLUTION,}$

$\sf\implies Perimeter = 2 ( Length + Breadth )$

$\sf\implies 56 = 2 \times (x + 2x - 8)$

$\sf\implies 56 = 2 \times (3x - 8)$

$\sf\implies \dfrac{56}{2}= 3x-8$

$\sf\implies \cancel \dfrac{56}{2}= 3x-8$

$\sf\implies 28=3x-8$

$\sf\implies 28+8= 3x$

$\sf\implies 36=3x$

$\sf\implies \dfrac{36}{3} =x$

$\sf\implies \cancel \dfrac{36}{3} =x$

$\sf\therefore x=12m$

$\large{\boxed{\bf{ \implies x(breadth)=12m}}}$

NOW, FORFINDING LENGTH,

AS GIVEN, LENGTH = 2X-8

$\sf\implies Length = 2(12) - 8$

$\sf\implies Length = 36 - 8$

$\sf\implies Length = 16 m$

$\large{\boxed{\bf{Y(breadth)=16m }}}$

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