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 metre^2 is Rs 10000, find the height of the hall.

Answer 1

Given perimeter of rectangular floor =200m

we will use formula of rectangle = 2(L+B)

2(L+B) = 200

L+B = 200 /2

L+B = 100m...... (1)

Area of four walls of room

= 2(lh +bh) = 2h (L+B) = 2h * 100 = 200hm²

Given: cost of painting per1m² = RS10

Cost of painting per 20hm²= 10,000

200h *10 = 10,000

h = 10,000 / 200*10

h = 5m

therefore height of the wall = 5m

Answer 2

Answer:

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

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

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

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

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

$\rule{300}{2}$

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

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

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

$\rule{300}{2}$

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

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

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

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

$\implies\bf h = 5m$