Question

the perimeter of a rectangular swimming pool is 154m .its length is 2m more than twice its breadth.what are the length and the breadth of the pool​

Answer 1

❍ 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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Answer 2

Given:

• the perimeter of a rectangular swimming pool is 154m
• its length is 2m more than twice its breadth.

To Find:

• breadth.what are the length and the breadth of the pool

Solution:

Here, we have given that the perimeter of the swimming pool is 154m and the length of the swimming pool is 2m more than twice of the breadth of the pool

Now,

• Let the Breadth of the pool be Xm

★as the length os 2m more that twice the breadth

• So, Length of the pool is 2x + 2m

As we know that,

${\longrightarrow }\tt \: perimeter \: of \: rectangle = 2(l + b)$

So, let's substitute the values now and simply the equation so that we will find the dimensions of the pool

${\longrightarrow }\tt \: perimeter = 2(l + b) \: \: \\ \\ \\ {\longrightarrow }\tt \: 154m = 2(x + 2x + 2) \: \: \: \: \\ \\ \\ {\longrightarrow }\tt \: 154m = 2(3x + 2) \: \: \: \: \: \: \: \: \: \: \\ \\ \\ {\longrightarrow }\tt \: 154m = 6x + 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ {\longrightarrow }\tt \: 6x = 154 - 4m \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ {\longrightarrow }\tt \: 6x = 150m \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ {\longrightarrow }\tt \: x = \cancel \frac{150m}{6} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \orange{\longrightarrow \tt \: x = 25m \bigstar} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now, Let's find the dimensions,

• Length of the pool = $\pink{ \tt \: 2x + 2 = 52m}$
• Breadth of the pool = $\pink{ \tt \: x = 25m}$

Hence,

• The dimensions are 52m and 25m

Diagram:

$\tt52m \: \: \: \: \: \: \: \: \: \: \: \\ \begin{gathered}\begin{gathered}\boxed{\begin{array}{}\bf { \red{}}\\{\qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{}\\ { \sf{ }}\\ { \sf{ }} \\ \\ { \sf{ }}\end{array}}\end{gathered}\end{gathered} \tt25m$

More Info:

★Area of a rectangle = length × breadth

★ Area of a square = side × side

★ Area of a triangle = ½ × base × hieght

★ Area of a rhombus = d₁ × d₂ / 2

★ Area of a parallelogram = base × hieght

★ Perimeter of square = 4 × side