Question

* The sides of a rectangular park are in the ratio 4:3. If its area is 1728 m. find the cost of
fencing it at rupee 30 per metre ​

Answer 1

$\huge\mathcal{\blue{Required-Answer}}$

$\small{\red{ABCD\: is\: a\: rectangular\: park}}$

$\small{\red{Consider\:AB\:and\: BC\: be\: the \:sides \:of\: the \:rectangle }}$

$AB\: :\: BC = 4:3$

$∴\:let\:AB\:=\:4x\\and\\BC\:=\:3x$

$area \: of \: rectangle\:=\:l×b$

$4x × 3x\: = \:1728$

$⇒12x^2\:=\:1728$

$⇒x^2\:=$ $\frac{1728}{2}$

$⇒x^2\:=\:144$

$⇒x\:=\: √144\:=\:12$

$\small{\red{Hence\: Length \:= \:4x\: = \:4×12 \:=\: 48m}}$

$\small{\red{Breadth\: = \:3x\: = \:3 × 12\: = \:36m}}$

$\small\underline{\red{∴\: Perimeter \:of \:a \:rectangle\: = \:2(l+b)}}$

$\small\mathtt{\green{⇒2\:(48+36) \:= 2\: × \:84\: = 168m}}$

$\small{\red{Cost\: of \:fencing \:=\: perimeter \:× Rate\:=}}$$\small\mathtt{\green{168 × 2.50}}$

$\small{\blue{The\:Total\:cost\:of\:fencing\:=\:Rs.\:420}}$

$\huge\boxed{\fcolorbox{blue}{lime}{Swipe↪}}$

Hope it helps

ThankQ

$\huge\mathcal{\pink{@ItzSwegBoi}}$

Answer 2

$\small{\red{ABCD\:is\:a\:rectangular\:park}}$

$\small{\red{Consider\:AB\:and\:BC\:be\:the\:sides\:of\:the\:rectangle}}$

$AB\: : \: BC\: = \: 4 : 3$

$∴let \: ab \: = 4x \: and \: bc \: = 3x \\ \\ \\ area \: of \: rectangle \: = l \times b \\ \\ 4x \: ×\:3x = 1728$

$=> \: 12 {x}^{2} = 1728 \\ =>{x}^{2} \: = \frac{1728}{2} \\ \\ => {x}^{2} \: = 144 \\ \\ =>x = \sqrt{144} = 12$

$hence \: length \: = 4x = 4 \times 12 = 48m \\ breath = 3x = 3 \times 12 = 36m \\ \\ ∴perimeter \: of \: a \: rectangle \: = 2(l + b) \\ \\ =>2(48 + 36) = 2 \times 84 = 168m$

$\small{\green{Cost\:of\:Fencing\: perimeter×rate\:=}}$

$\small\mathtt{\red{168\:×\:2.50}}$

$\small{\blue{The\:total\:cost\:of\:fencing\:=\:420}}$

$\huge\boxed{\fcolorbox{blue}{yellow}{Swipe☞︎︎︎}}$