Question

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per m² a year. A company hired one of its walls for 6 months. How much rent did it pay?

Answer 1

Let the sides of a triangular walls are a = 13 m, b = 14 m and c = 15 m.

Now, the semi-perimeter of triangular side wall,

`s = (a + b + c)/2`

= `(13 + 14 + 15)/2`

= 21 m

Now, area of triangular wall = `sqrt(s(s - a)(s - b)(s - c))`  ...[By Heron’s formula]

= `sqrt(21(21 - 13)(21 - 14)(21 - 15))`

= `sqrt(21 xx (21 - 13) xx (21 - 14) xx (21 - 15))`

= `sqrt(21 xx 8 xx 7 xx 6)`

= `sqrt(21 xx 4 xx 2 xx 7 xx 3 xx 2)`

= `sqrt(21^2 xx 4^2)`

= 21 × 4

= 84 m² 

The advertisement yield earning per year for 1 m² area is Rs. 2000.

Therefore, advertisement yield earning per year on 84 m² = 2000 × 84 = Rs. 168000.

According to the question, the company hired one of its walls for 6 months, therefore company pay the rent = `1/2 xx 168000` = Rs. 84000.

Hence, the company paid rent Rs. 84000.