Question

The triangular side walls of a flyover have been used for advertisements. The
be the area of the signal board?
2.
the walls are 122 m, 22 m and 120 m (see Fig. 12.9). The advertisements y
earning of 5000 per m per year. A company hired one of its walls for 3 month
much rent did it pay?
122m
22m
120m
Fig. 12.9​

Answer 1

⇒ Given:

→ The three sides of a triangular wall have the measures 122 m, 22 m and 120 m.

→ The cost of putting an ad on it for 1 m² per year is Rs 5000.

→ A company hired one of its walls for 3 months.

⇒ To Find:

The total rent the company has to pay.

⇒ Formula to use:

→ $\sf{\sqrt{S(S-a)(S-b)(S-c)}}$

⇒ Required Values:

→ Side a = 122 m

→ Side b = 22 m

→ Side c = 120 m

$\sf{Semiperimeter=\dfrac{a+b+c}{2}}$

$\sf{=\dfrac{122+22+120}{2}}$

$\sf{=\dfrac{264}{2}}$

→  = 132 cm

→ S - a = 132 - 122 = 10 cm

→ S - b = 132 - 22 = 110 cm

→ S - c = 132 - 120 = 12 cm

⇒ Solution:

In order to find the total area required for the ad, we need to apply the Heron's Formula.

$\sf{=\sqrt{S(S-a)(S-b)(S-c)}}$

$\sf{=\sqrt{132\times10\times110\times12}}$

$\sf{=\sqrt{11\times12\times10\times11\times10\times12}}$

$\sf{=11\times12\times10}$

= 1320 m²

Now, we know that the company hired the wall for 3 months.

Rent of hiring 1 m² for 1 year = Rs 5000/m²

Rent of hiring 1 m² for 1 month = 5000/12

Rent of hiring 1 m² for 3 months = $\sf{\dfrac{5000}{12}\times3}$

So,

Rent of hiring 1320 m² for 3 month = $\sf{\dfrac{5000}{12}\times3\times1320}$

$\sf{=\dfrac{5000}{4}\times1320}$

$\sf{=1250\times1320}$

= 16,50,000

Hence the required rent is Rs 16,50,000.

Knowledge Bytes:

→ Heron's Formula

The Heron's Formula which was proposed by the mathematician Heron allows us to find the area of any kind of triangle using the formula:

$\sf{\sqrt{S(S-a)(S-b)(S-c)}}$