Question

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

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\sf\bullet perimeter= 154m\\ \\ \sf\bullet Breadth =x\\ \\ \sf\bullet Length=2x+2$

Now we have to find the length and breadth of pool

$\boxed{\dag{\sf{\:\: Perimeter\:of\: rectangle=2(l+b)}}}$

$\bf\underline{\underline{\red{A.T.Q:-}}}$

$\sf\implies 2(2x+x+2)=154\\ \\ \sf\implies 3x+2=\cancel{\dfrac{154}{2}}\\ \\ \sf\implies x=77-2\\ \\ \sf\implies 3x= 75\\ \\ \sf\implies x=\cancel{\dfrac{75}{3}}\\ \\ \sf\implies x=25m$

$\sf\bullet breadth= 25m\\ \\ \sf\bullet length= 2\times 25+2\\ \sf\implies 50+2=52$

$\boxed{\sf{Length=52m\:\:and\:\: breadth=25m}}$

Answer 2

$\large{\underline{\mathsf{\red{Answer-}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{\bold{Length\:of\:swimming\:pool\:is\:52\:m.}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\underline{\bold{Breadth\:of\:swimming\:pool\:is\:25\:m.}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large{\underline{\mathsf{\red{Explanation-}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\begin{lgathered}\bold{Given} \begin{cases}\sf{Perimeter\:of\:rectangular\:pool\:=\:154\:m} \\ \sf{Length\:is\:2\:m\:more\:than\:twice\:its\:breadth}\\ \sf{Length\:and\:breadth\:of\:pool\:=\:?}\end{cases}\end{lgathered}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf{Let\:breadth\:of\:pool\:be\:B}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\small{\sf{\purple{(According\:to\:the\:question-)}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf{Length\:=\:2B\:+\:2}$ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀– eq (1)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

We know that,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large{\boxed{\blue{\sf{Perimeter\:of\:rectangle\:=\:2(L+B)}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\small{\pink{\sf{(Putting\:the\:values-)}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

: $\implies$ $\sf{154\:=\:2(2B\:+\:2\:+B)}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

: $\implies$ $\sf{154\:=\:4B\:+\:4\:+\:2B}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

: $\implies$ $\sf{154\:-\:4\:=\:6B}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

: $\implies$ $\sf{6B\:=\:150}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

: $\implies$ $\sf{B\:={\cancel{\dfrac{150}{6}}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

: $\implies$ $\sf{B\:=\:25\:m}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\therefore$ $\underline{\bold{Breadth\:of\:swimming\:pool\:is\:25\:m.}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\rule{200}2$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\sf{Now,\:put\:the\:value\:of\:B\:in\:eq\:(1)}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

: $\implies$ $\sf{Length\:of\:pool\:=\:2(25)\:+\:2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

: $\implies$ $\sf{Length\:of\:pool\:=\:50\:+\:2}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

: $\implies$ $\sf{Length\:of\:pool\:=\:52\:m}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\therefore$ $\underline{\bold{Length\:of\:swimming\:pool\:is\:52\:m.}}$