Question

The perimeter of a rectangular swimming pool is 154 m. its length is 2m more than twice its breadth. What are the length and the breadth of the pool? Find

Answer 1

Answer:

Given :-

• The perimeter of a rectangular swimming pool is 154 m. It's length is 2 m more than twice of its breadth.

To Find :-

• What is the length and breadth of rectangular swimming pool.

Formula Used :-

$\sf\boxed{\bold{\pink{Perimeter\: of\: Rectangle =\: 2(Length + Breadth)}}}$

Solution :-

Let, the breadth be x m

And, the length will be 2x + 2

According to the question by using the formula we get,

↦ $\sf 2(2x + 2 + x) =\: 154$

↦ $\sf 4x + 4 + 2x =\: 154$

↦ $\sf 6x =\: 154 - 4$

↦ $\sf 6x =\: 150$

↦ $\sf x =\: \dfrac{\cancel{150}}{\cancel{6}}$

➠ $\sf\bold{\green{x =\: 25\: m}}$

Hence, the length and breadth are :

✪ Length of swimming pool :

↦ $\sf 2x + 2\: m$

↦ $\sf 2 \times 25 + 2\: m$

↦ $\sf 50 + 2\: m$

➠ $\sf\bold{\red{52\: m}}$

And,

✪ Breadth of swimming pool :

↦ $\sf x\: m$

➠ $\sf\bold{\red{25\: m}}$

$\therefore$ The length and breadth of a rectangular swimming pool is 52 m and 25 m respectively.

Answer 2

❍ Let's Consider breadth of Rectangular swimming pool be x .

Given that ,

⠀⠀⠀⠀⠀It's length is 2m more than twice its breadth .

Then ,

• Length of Rectangular swimming pool is 2 + 2x .

$\underline {\frak{\dag As \:We \:know \:that \: : }}$

$\qquad \qquad \qquad \underline {\boxed {\sf{ \bigstar Perimeter _{(Rectangle)} = 2 (l + b) \:units}}}$

Where ,

• l is the Length of Rectangle in m and b is the Breadth of Rectangle in m and We have given with the Perimeter of Rectangle is 154 m .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \qquad:\implies \sf{ 154 m = 2 ( x + 2 + 2x )}$

$\qquad \qquad:\implies \sf{ \dfrac{\cancel {154}}{\cancel {2}} = x + 2 + 2x }$

$\qquad \qquad:\implies \sf{ 77 = x + 2 + 2x }$

$\qquad \qquad:\implies \sf{ 77 = 2 + 3x }$

$\qquad \qquad:\implies \sf{ 77 - 2 = 3x }$

$\qquad \qquad:\implies \sf{ 75 = 3x }$

$\qquad \qquad:\implies \sf{ \dfrac{\cancel {75}}{\cancel {3}} = x }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  x = 25\: m}}}}\:\bf{\bigstar}$

Therefore,

• Length of Rectangle is 2 + 2x = 2 + 2 × 25 = 50 + 2 = 52 m .

• Breadth of Rectangle is x = 25 m .

Therefore,

⠀⠀⠀⠀⠀$\therefore{\underline{\mathrm {  Length \:and\:Breadth \:of\:Rectangular \:swimming \:pool\:is\:\bf{52m\:and\:25 m\:}\: \: ,respectively. }}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\large {\boxed{\sf{\mid{\overline {\underline {\star Verification \::}}}\mid}}}$

$\underline {\frak{\dag As \:We \:know \:that \: : }}$

$\qquad \qquad \qquad \underline {\boxed {\sf{ \bigstar Perimeter _{(Rectangle)} = 2 (l + b) \:units}}}$

Where ,

• l is the Length of Rectangle in m and b is the Breadth of Rectangle in m and We have given with the Perimeter of Rectangle is 154 m .

⠀⠀⠀⠀⠀⠀$\underline {\bf{\star\:Now \: By \: Substituting \: the \: Given \: Values \::}}$

$\qquad \qquad:\implies \sf{ 154 m = 2 ( 25 + 52 )}$

$\qquad \qquad:\implies \sf{ 154 m = 2 ( 77 )}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  154m = 154\: m}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀$\therefore \bf{\underline {Hence,\:Verified \;}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

Diagram :

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large 52\: m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large 25\: m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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