Question

the length of a rectangular field is four times its bredth if a perimeter of a field is 900m find the lingth and bredth​

Answer 1

$\huge{ \red{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: SOLUTION \: \: \red{ \mid}}}}}}}}$


$\underline{ \underline{ \bold{ \: \:GIVEN\: \: : }}} \to \\ \\ \bold{Length \: \: of \: \: the \: \: rectangular \: field \: \: is} \\ \\ \bold{4 \: \: times \: \: than \: \: its \: breadth.} \\ \\ \\ \bold{Perimeter \: \: of \: \: the \: \: field = 900 \: m}$


$\bold{Let,} \\ \\ \bold{Breadth \: \: of \: \:the \: \: rectangular \: \: field = x \: \: metre } \\ \\ \bold{ \therefore \: Length \: \: of \: \: the \: \: rectangular \: \: field = 4x \: \: metres}$


$\underline{ \underline{ \bold{ \: \: We \: \: know \: \: that \: \: } }}\: \\ \\ \boxed{\bold{2 \: ( \: Length \: + \: Breadth \: ) = Perimeter}}$


$\underline{ \bold{ \: \: According \: \: To \: \:Question \: \: } } \\ \\ \bold{2 \: ( \: 4x \: + \: x \: ) = \: 900} \\ \\ \bold{ \Longrightarrow \: 2 \: \times \: 5x \: = \: 900 } \\ \\ \bold{ \Longrightarrow \: 10x \: = \: 900} \\ \\ \bold{ \Longrightarrow \: x \: = \: \frac{900}{10} } \\ \\ \bold{ \therefore \: \: x \: = \: 90} \\ \\ \bold{ \therefore \: \: 4x = 4 \times 90 = 360}$


$\bold{Hence,} \\ \\ \bold{Length \: \: of \: \: the \: rectangular \: \: field = 360 \: m} \: \\ \\ \bold{Breadth \: \: of \: \: the \: \: rectangular \: \: field = 90}$


$\huge{ \red{ \underline{ \overline{ \mid{ \bold{ \purple{ \: \: ANSWER \: \: \red{ \mid}}}}}}}}$


$\boxed{ \bold{ \pink{ \: Length = 360 \: \: m \: \: \: and, \: \: \: Breadth = 90 \: m}}}$

Answer 2

SOLUTION

Let,

Breadth of the rectangular field = b

•°• Length of the rectangular field = 4b

Given,

Perimeter of the rectangular field = 900 m

According to the question,

2 ( length + breadth ) = 900

=> length + breadth = 900 / 2

=> length + breadth = 450

=> 4b + b = 450

=> 5b = 450

=> b = 450 / 5

•°• b = 90

=> 4b = 4 × 90 = 360

Hence ,

Length of the rectangular field = 360 m

And ,

Breadth of the rectangular field = 90 m