Question

The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹10 per m2 is ₹15000, find the height of the hall.

Answer 1

Base perimeter = 2×(l+b) = 250 m
Total area painted = L.S.A
= Total Money spent on painting÷ Rate of painting 1 m ²
 = 15000 ÷ 10  = 1500 m ²
L.S.A = 2×(l+b)×h
 250 × h = 1500 m²
h = 1500 ÷ 250 = 6 m
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Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Given

${\boxed{\sf\:{Perimeter= 250\;metre}}}$

Hence we have

2(l + b) = 250 metre

Now

${\boxed{\sf\:{We\;have\;to\;assume}}}$

Height of hall = h metre

Hence,

${\boxed{\sf\:{Area\;to\;be\;painted}}}$

= 2(l + b)h

${\boxed{\sf\:{Area\;portion\;to\;be\;painted}}}$

$\tt{\rightarrow\dfrac{Combined\;Cost}{Rate\;per\;m^2}}$

$\tt{\rightarrow\dfrac{15000}{10}}$

= 15000 m²

Hence we have

2(l + b) = 1500 m²

${\boxed{\sf\:{Substitute\;the\;values}}}$

250 × h = 1500

$\tt{\rightarrow h=\dfrac{1500}{250}}$

h = 6

Hence we get

$\Large{\boxed{\sf\:{Height\;of\;hall = 6\;metre }}}$