Question

Perimeter of a rectangular field is 1280m. The ratio between its side is 3:4 . Find its length.

Answer 1

Correct Question:-

• Perimeter of a rectangular field is 1280 m. The ratio between its side is 3:2. Find its length.

⠀

Given:-

• Perimeter of a rectangular field is 1280 m.
• The ratio between its side is 3:2.

⠀

To find:-

• Find its length.

⠀

Solution:-

Let,

• the length be 3x.
• the breadth be 2x.

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→ Perimeter = 2(length + breadth)

→ 2(l + b) = 1280

→ 2(3x + 2x) = 1280

→ 2(5x) = 1280

→ 5x = 1280/2

→ 5x = 640

→ x = 640/5

→ x = 128

Therefore,

• Length = 3x = 3× 128 = 384 m
• Breadth = 2x = 2×128 = 256 m

Answer 2

Correct Question-:

• Perimeter of a rectangular field is 1280m. The ratio of its length and breadth is 3:2 . Find its length and breadth.

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{  Length \:and\:Breadth \:of\:Rectangular \:field \:are\:384m\:and\:256m\:respectively.}}}}}$

Explanation-:

• $\mathrm { Given-:}$

• Perimeter of a rectangular field is 1280m.
• The ratio of its length and breadth is 3:2 .

• $\mathrm { To\:Find-:}$

• The exact measure of length and breadth of Rectangular field.

$\dag{\mathrm { Solution \:of\:Question \:-:}}$

• $\mathrm { Let's \:Assume-:}$

• The length of Rectangular field be 3x .
• The breadth of Rectangular field be 2x .

Then ,

• $\frak{Dimensions \:\: -:} \begin{cases} \sf{Length \:of\:Rectangular \:Field \:=\:\frak{3x\:m}}& \\\\ \sf{Breadth \:of\:Rectangular \:Field \:=\:\frak{2x\:m}}\end{cases}$

• $\underbrace { \mathrm { Understanding \: the \: Concept \:-:}}$

• We have to find the length and breadth of Rectangular field ,

• For this we have to put the assumed values in Formula of Perimeter of Rectangle,

• From that we can find the exact measure of Length and Breadth.

As , We know that ,

• $\underline{\boxed{\star{\sf{\blue{  Perimeter \:of\:Rectangular \:plot\: = 2( Length+ Breadth).}}}}}$

• $\frak{Here \:\: -:} \begin{cases} \sf{The\:Perimeter \:of\:Rectangular\:Field \:is\:= \frak{1280\:m}} & \\\\ \sf{Length \:of\:Rectangular \:Field \:=\:\frak{3x\:m}}& \\\\ \sf{Breadth \:of\:Rectangular \:Field \:=\:\frak{2x\:m}}\end{cases}$

Now by putting known Values-:

• $\longrightarrow {\mathrm { 2 ( 3x + 2x ) = 1280 m}}$

• $\longrightarrow {\mathrm { 2 ( 5x ) = 1280 m}}$

• $\longrightarrow {\mathrm { 5x = \dfrac{1280}{2} }}$

• $\longrightarrow {\mathrm { 5x = \dfrac{\cancel {1280}}{\cancel {2}} }}$

• $\longrightarrow {\mathrm { 5x = 640}}$

• $\longrightarrow {\mathrm { x =\dfrac{ 640}{5}}}$

• $\longrightarrow {\mathrm { x = 128}}$

Therefore,

• $\boxed {\mathrm { x = 128}}$

Now By Putting x = 128 ,

• $\frak{Putting \:x=128\: -:} \begin{cases} \sf{Length \:of\:Rectangular \:Field \:=\:\frak{3x\:=3 \times 128 =384 m}}& \\\\ \sf{Breadth \:of\:Rectangular \:Field \:=\:\frak{2x\:=2\times 128 =256 m}}\end{cases}$

Hence ,

• $\underline{\boxed{\star{\sf{\blue{  Length \:and\:Breadth \:of\:Rectangular \:field \:are\:384m\:and\:256m\:respectively.}}}}}$

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