Question

The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see Fig. 12.9). The advertisements yield an earning of ` 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?

Answer 1

Answer:

Rs 1650000 !!

Step-by-step explanation:

Let ,

• a = 122 m
• b = 22m
• c = 120 m

Half of Perimeter (s) :

$\longrightarrow\boxed{ \sf \: S = \frac{a + b + c}{2} } \\ \\ \longrightarrow\sf \: S = \frac{122 + 22 + 120}{2} \\ \\ \longrightarrow\sf \: S = \cancel \frac{264}{2} \\ \\ \longrightarrow\sf S = \boxed{ \green{132 \: cm}}$

Area of a Wall :

$\rightarrow \boxed{ \sf \: \sqrt{S(S - a)(S - b)(S - c)} } \\\\\implies \sqrt{132(132 - 122)(132 - 22)(132 - 120)} \\ \\ \implies\sqrt{132 \times 10 \times 110 \times10 } \\ \\ \implies \sqrt{11 \times 12 \times 12 \times 11 \times 10 \times 10} \\ \\ \implies 11 \times 12 \times 10 \\ \\ : \implies \boxed{ \green{1320 \: { \sf \: m {}^{2} }}}$

According to Question :-

$= \cancel{1320 }\times 5000 \times \frac{3}{ \cancel{12}} \\ = 110 \times 5000 \times 3 \\ : \implies \boxed{ \green{₹ \: 1650000}}$

Note : Slide to left to view full Solution!!

_______________________

☆ Some Important formulae Related to this Chapter :

◇ Heron's Formula

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

Here S

• $\sf \: S = \frac{a + b + c}{2}$

S is Known as Half of Perimeter

Here, a, b, c are side of a Triangle.

◇ Area of a Triangle

• $\sf\frac{1}{2} × Base × height$

••••♪♪

Answer 2

Answer:-

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

Step-by-step explanation:

Given that:-

The side walls of a flyover which have been used for advertisements are triangular in shape.The length of Wall are 122m,22m and 120m.

As (122)² = 14884 = (122)² + (120)²

i.e. , By Pythagoras theorem, the walls in the shape of right triangles.

• The advertisements yield an earning of ₹5000 per m² per year.
• A company hired bone of its walls for 3 months.

To find:

• How much did the rent paid by the company for 3 months?

Before solving question we must to know this formula:-

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. Ans.

I hope it's help you...☺