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

Answer:

Length of rectangle = 60 Cm

Breadth of rectangle = 80 Cm

Step-by-step explanation:

Given----> Length and breadth of a rectangular field are in the ratio 3 : 4 and perimeter of field is 280 Cm .

To find-----> Length and breadth of rectangle

Solution-----> ATQ,

Ratio of length and breadh is 3 : 4 .

Let , Length of rectangle = 3x

Breadth of rectangle = 4x

We know that ,

Perimeter of rectangle = 2 ( Length + Breadth )

ATQ, Perimeter of rectangle = 280 Cm

So,

=> 280 = 2 ( 3x + 4x )

=> 280 / 2 = 7x

=> 140 = 7x

=> x = 140 / 7

=> x = 20

Length of rectangle = 3 x

= 3 ( 20 )

= 60 Cm

Breadth of rectangle = 4 x

= 4 ( 20 )

= 80 Cm

Answer 2

Answer:-

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

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

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

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

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

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

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

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

$\large\red{\underline{\boxed{\textsf{\color{darkgreen}{Explantion:-}}}} }$

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

$<font color =green>$

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

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

|:$\implies\sf140 = 7a$

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

|:$\implies\sf A = 20$

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

$<font color =purple>$

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

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

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

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