Question

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Question 8:- The triangular side wall of a flyover have been used for advertisement. The side of the walls are 122m,
22m and 120m (see figure). The advertisement yields an earning of Rs.5000 per m² per year. A company
hired one of its walls for 3 months. How much rent did it pay?
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Answer 1

Answer:

The area of the triangular wall = 1/2 × b× h

= 1/2 × 120 × 22

= 1320 m²

Cost of advertising at rate of 5000 per m² for a year= Rs.5000 × 1320

= Rs. 66,00,000

There 4 quarter in 1 year and each quarter has 3 months

thus, 6600000÷4

= Rs. 16,50,000

Therefore the cost of advertising for 3 months is rs. 16,50,000

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Answer 2

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.

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