Jun 20, 2016

6 metres

#### Explanation:

Metaphorically speaking, open up the hall like a box so that all the walls form 1 rectangle. We are given the length of this rectangle as 250m

Known
Total cost $\to 15000$
Cost for each $1 {m}^{2} \to 10$
Perimeter $\to 250 m$

Let the total surface area of the wales be $a$
Let the height of the walls be $h$ then

$a = 250 h$
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$\textcolor{b l u e}{\text{Method plan}}$

$\textcolor{b r o w n}{\text{Step 1:}}$ Determine how many $1 {m}^{2}$ there are using cost.

$\textcolor{b r o w n}{\text{Step 2:}}$ Use the total area to determine height.

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Solving for step 1}}$

Total ${m}^{2} \to \left(\text{total cost")/("cost per square metre}\right) = \frac{15000}{10} = 1500 {m}^{2}$

,..............................................................................
$\textcolor{b l u e}{\text{Solving for step 2}}$

$\textcolor{b r o w n}{a = 255 h} \textcolor{b l u e}{\to 1500 = 250 h}$

Divide both sides by 250

$\frac{1500}{250} = \frac{250}{250} h$

But $\frac{250}{250} = 1$

$h = 6 \text{ metres}$

Approximately 19.7 feet high. That's a lot of wall !