Question

length and breadth of a reactangular plot are in the ratio 3:2 and the perimeter is 300 m

Answer 1

AnswEr -:

• $\underline {\mathrm {\pink { The\: Length \:and\:Breadth \:are\:90m\:and\:60m\:,respectively}}}$

Explanation-:

$\mathrm {\bf{ Given-:}}$

• Length and Breadth of a rectangular plot are in the ratio 3:2.

• The Perimeter of Rectangular plot is 300 m

$\mathrm {\bf{To\:Find-:}}$

• The Length and Breadth of Rectangular plot .

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

$\mathrm {\bf{Let's \:Assume -:}}$

• The Length and Breadth of Rectangular plot be 3x and 2x .

Therefore,

• $\mathrm{\bf{\blue {Dimensions \:are\:\: -:}}} \begin{cases} \sf{\blue{The\:Length \:of\:the\:Rectangular \:plot \:is\:= \frak{3x\:m}}} & \\\\ \sf{\red{Breadth \:of\: Rectangular \:plot\:is \:=\:\frak{2x \: m}}}\end{cases}$

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

• We have to find the Dimensions [ Length and Breadth ] of Rectangular plot when Perimeter and ratios of Length and Breadth is given .

• Firstly put the assumed values [ Length and Breadth ] in the Formula for Perimeter of Rectangle.

• By this We can get the Dimensions [ Length and Breadth ] of Rectangular plot .

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$\dag{\mathrm {\bf{Finding\:Length \:and\:Breadth \:of\: Rectangular \:Plot \:-:}}}$

As, We know that ,

• $\underline{\boxed{\star{\sf{\blue{Perimeter _{(Rectangle)}  \: = \: 2 ( Length + Breadth) \:units}}}}}$

• $\mathrm{\bf{\blue {Here\:\: -:}}} \begin{cases} \sf{\blue{The\:Length \:of\:the\:Rectangular \:plot \:is\:= \frak{3x\:m}}} & \\\\ \sf{\red{Breadth \:of\: Rectangular \:plot\:is \:=\:\frak{2x \: m}}}& \\\\ \sf{\pink{ Perimeter \:of\: Rectangular \:plot\:is \:=\:\frak{300m}}}\end{cases}$

Now , By Putting known Values in Formula for Perimeter of Rectangle-:

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 2(3x+2x) = 300m }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 3x+2x = \dfrac{300}{2} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 3x+2x = \dfrac{\cancel {300}}{\cancel {2}} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 3x+2x = 150 }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 5x = 150 }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { x = \dfrac{150}{5} }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { x = \dfrac{\cancel {150}}{\cancel {5}} }}$

• $\qquad \quad \qquad \quad \underline {\boxed{\mathrm {\pink{ x = 30 }}}}$

Putting x = 30 in Assumed Length and Breadth-:

• $\mathrm{\bf{\blue {Putting \:x = 30 \: -:}}} \begin{cases} \sf{\blue{The\:Length \:of\:the\:Rectangular \:plot \:is\:= \frak{3x\:= \:3 \times 30 = 90 m}}} & \\\\ \sf{\red{Breadth \:of\: Rectangular \:plot\:is \:=\:\frak{2x= 2 \times 30 \:= 60 m}}}\end{cases}$

Hence ,

• $\underline {\mathrm {\pink { The\: Length \:and\:Breadth \:are\:90m\:and\:60m\:,respectively}}}$

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$\Large {\bf{\mathrm {Verification \:\red{♡}\:-:}}}\|$

As , We know that ,

• $\underline{\boxed{\star{\sf{\blue{Perimeter _{(Rectangle)}  \: = \: 2 ( Length + Breadth) \:units}}}}}$

• $\mathrm{\bf{\blue {Here\:\: -:}}} \begin{cases} \sf{\blue{The\:Length \:of\:the\:Rectangular \:plot \:is\:= \frak{90\:m}}} & \\\\ \sf{\red{Breadth \:of\: Rectangular \:plot\:is \:=\:\frak{60 \: m}}}& \\\\ \sf{\pink{ Perimeter \:of\: Rectangular \:plot\:is \:=\:\frak{300m}}}\end{cases}$

Now , By Putting known Values in Formula for Perimeter of Rectangle-:

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 2(90+60) = 300m }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 2(150) = 300m }}$

• $\qquad \quad \qquad \quad \longmapsto {\mathrm { 300m = 300m }}$

Therefore,

• $\qquad \quad \qquad \quad :\implies {\mathrm { L.H.S = R.H.S }}$

• $\qquad \quad \qquad \quad :\implies {\mathrm { Hence \:, Verified \: ! }}$

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$\large{\boxed {\bf{\mathrm|\:\:{\underline {More \:to\:know-:}}\:\:|}}}$

• Area of Rectangle = Length × Breadth sq.units

• Area of Square = Side × Side sq.units

• Area of Triangle = ½ × Base × Height sq.units

• Area of Trapezium = ½ × Height × (a+b) or Sum of Parallel sides sq.units

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