Question

"Question 2 The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of Rs 5000 per m 2 per year. A company hired one of its walls for 3 months. How much rent did it pay?

Class 9 - Math - Heron's Formula Page 202"

Answer 1

The perimeter of a triangle is equal to the sum of its three sides it is denoted by 2S.
2s=(a+b+c)
s=(a+b+c)/2

Here ,s is called semi perimeter of a triangle.

The formula given by Heron about the area of a triangle is known as Heron's formula.

According to this formula area of a triangle= √s (s-a) (s-b) (s-c)

Where a, b and c are three sides of a triangle and s is a semi perimeter.

This formula can be used for any triangle to calculate its area and it is very useful when it is not possible to find the height of the triangle easily .
Heron's formula is generally used for calculating area of scalene triangle.
___________________ _______________

Solution:

Let the sides of the triangle are a=122 m, b=22 m & c= 120 m.

Semi Perimeter of the ∆,s = (a+b+c) /2
s=(122 + 22 + 120) / 2
s= 264/2= 132m

Using heron’s formula,

Area of the wall = √s (s-a) (s-b) (s-c)

= √132(132 – 122) (132 – 22) (132 – 120)

= √132 × 10 × 110 × 12
=√11×12×10×11×10×12
=√11×11×12×12×10×10
= 11×12×10
= 1320m²

Given, earning on 1m² per year= ₹5000

Earning on 1320 m² per year=1320×5000= ₹6600000

Now, earning in 1320 m² in 12 months= ₹6600000

earning in 3 months = ₹ 6600000 ×3/12 = ₹ 1650000

Hence, the rent paid by the company for 3 months is ₹ 1650000.

=======================================