Question

length and breadth of a rectangular field are in the ratio 3:4 if perimeter of field is 280cm find length and breadth.​

Answer 1

Step-by-step explanation:

Here,

let the of length and breadth of rec field = 3x and 4x respectively ,

Then,

according to formula ,

perimeter of rec = 2( l + b)

280 cm = 2( 3x + 4x)

280 = 14x

x = 280/14

X = 20 cm

Hence,

length = 3x = 3x 20 = 60 cm

breadth = 4x = 4 x 20 = 80 cm

answered

Answer 2

$\huge \underline \mathtt \red{SOLUTION:-}$

$\small\orange{\underline{\boxed{\sf \red{Lenght\: of \:rectangle = 60cm} }}}$

$\small\red{\underline{\boxed{\sf \orange{Breadth\: of\: rectangle = 80cm }}}}$

$\frak\red{Given}\begin{cases}\sf\red{\underline{Ratio=3:4}} \\ \sf\blue{\underline{perimeter\: of \:field =280cm}} \\\sf\green{\underline{Lenght \:of \:rectangle \:= ?}}\\\sf\orange{\underline {Breadth\: of \:rectangle = ?}}\end{cases}$

$\large\underline\frak{\green{Suppose:- }}$

$\small\underline\textsf{ \purple{length of rectangle be} = \red{3A}}$

$\small\underline\textsf{ \pink{Breadth of rectangle be} = \red{4A}}$

$\large\underline\textsf{\red{ Formula used} }$

$\footnotesize\sf{\purple{ perimeter \: of \: rectangle = \boxed{\tt 2(length \: \: + breadth}}}$

$\huge \underline \mathtt \green{ExPlanation:-}$

$\small\underline\textsf{ \orange{Cross Multiplication }}$

|:$\implies\sf280 = 2(3a + 4a)$

|:$\implies\sf \frac{280}{2} = 7a \:$

|:$\implies\sf140 = 7a$

|:$\implies\sf A ={\cancel{\dfrac{140}{7} }}$

|:$\implies\sf A = 20$

$\small\underline\textsf{ Now, }$

$\leadsto\sf length \: of \: rectangle = 3a \\\sf\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3 \times 20 \\\sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \: \: \: = 60cm \\ \leadsto\sf breadth \: of \: rectangle = 4a \\\sf \: \: \: \:\:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4 \times 20 \\\sf \: \: \: \:\:\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 80cm}$

$\small\underline\textsf{ So, }$

$\small\orange{\underline{\boxed{\sf \red{Lenght\: of \:rectangle = 60cm}}}}$

$\small\red{\underline{\boxed{\sf \orange{Breadth\: of\: rectangle = 80cm }}}}$