Question

the floor of a rectangular hall has a perimeter of 200. if the cost of painting the four walls at the rate of rs 10 per m^2 is rs 10000, find the height of the hall

Answer 1

$\huge\mathbb{SOLUTION:-}$

• Given that the perimeter of rectangular hall =200m

• cost of painting 4 walls = Rs.10000

• Now find the area of 4 walls

$\sf\implies Area\:of\:4\:walls=\cancel{\frac{10000}{10}}=1000$

• Area of 4 walls =1000 square metre

$\boxed{\sf{Area\:of\:4\:walls=2(l+b)\times h}}$

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

$\sf\implies 2(l+b)h=1000\\ \\ \sf Put\: the\: value\:of\:2(l+b)\\ \\ \sf which\:is\:200\\ \\ \sf\implies 200\times h=1000\\ \\ \sf\implies h=\cancel{\frac{1000}{200}}\\ \\ \sf\implies h=5m$

$\boxed{\sf{\red{Height\:of\:hall=5m}}}$

Answer 2

Answer:

$\huge\underline\textsf{Height of Hall=5m}$

$\tt{Given}\begin{cases}\tt{perimeter=200m} \\ \tt{cost \:of \:painting \:4 \:wall =10,000} \\\tt{Area\: of \:wall =?}\end{cases}$

$\huge\underline\textsf{Explantion:- }$

$\implies\boxed{\bf area \: of \: 4 \: walls = \frac{1\cancel{0000}}{10} = 1000}$

$\large\underline\textsf{Area \:of \:wall =1000square\: meter}$

$\rule{300}{2}$

$\small\underline\textsf{Formula \:used }$

$\implies\bf area \: of \: 4 \: wall = 2(l + b) \times h$

$\implies\bf perimeter \: of \: rectangle = 2(l + b)$

$\rule{300}{2}$

$\implies\bf2(l + b) = 1000$

$\implies\bf put \: the \: value \: of \: 2(l + b) \\ \bf which \: is \: 200$

$\implies\bf 200 \times h = 1000$

$\implies\bf h = \frac{\cancel1\cancel0\cancel0\cancel0}{\cancel 2\cancel0\cancel0}$

$\implies\bf h = 5m$