# Question #c260f

Feb 15, 2018

Height of the room is $= 6 m t s$

#### Explanation:

Given -
Length of the room $= 12 m$
Cost of preparing the wall$= 1.35$/ ${m}^{2}$
Total cost of preparing the wall $= 340.20$
Cost of matting the floor$= 0.85$/ ${m}^{2}$
Total Cost of Matting the floor $= 91.80$ Let Lenth of the floor be $= l$
Let the width of the floor be $= b$
Then, the area of floor $= l \times b = l b$

Cost of matting the floor$= 0.85$/ ${m}^{2}$
Total Cost of Matting the floor $= l b \times 0.85 = 0.85 l b$
Since length is $12 m$Total Cost of Matting the floor $= 12 \times b \times 0.85 = 10.20 b$

$10.20 b = 91.80$
$b = \frac{91.80}{10.20} = 9 m$

There are four walls.
Let the height of the wall be$= h$
Total area of wall is $= \left[2 \left(l + b\right)\right] \times h$

$= \left[2 \left(12 + 9\right)\right] \times h = \left[2 \left(21\right)\right] \times h = 42 h . {m}^{2}$
Total cost of preparing the wall $= 42 h \times 1.35 = 56.7 h$

$56.7 h = 340.20$
$h = \frac{340.2}{56.7} = 6 m$

Height of the room is $= 6 m t s$