Question

If $780$ m${}^2$ of cloth is required to construct a $30$ cm long tent of base $10$ cm, the height of the tent will be ?

• A. $13$ cm
• B. $12$ cm
• C. $15$ cm

Answer 1

The correct option is B $12$ cm

We have a tent with the following dimensions:


Let us consider the height of the tent as $h$ cm and we can construct a perpendicular bisector of the triangular part to denote the height as given below.


Now, the cloth is used in the two sides of the tent, so the sum of the areas of $2$ rectangular sides $=$ amount of cloth required.

$⟹780=$ sum of areas of $2$ sides
$\therefore$ Area of one rectangular side $=\frac{780}{2}=390c{m}^2$

Since the length of the recatangle is $30$ cm and area $390$ cm${}^2$
breadth of the rectangular part $=\frac{390}{30}=13cm$
$(\because \text{Here, breadth of the rectangle = hypotenuse of the triangle})$


Therefore, by pythagoras theorem, the height $h$ of the tent $=\sqrt[2]{2{13}^2-5^2}=\sqrt[2]{2169-25}=\sqrt[2]{2144}$
$=12$ cm