Question

A triangular park in a city has dimensions
100 m x 90 m x 110 m. A contract is given to a
company for planting grass in the park at the rate
of 34000 per hectare. Find the amount to be paid​

Answer 1

Answer :

Amount to be paid = 14,422.8

Explanation :

According to the condition :

⟶ Area of the Triangle = Δ = √ s ( s - a ) ( s - b ) ( s - c )

⟶ ' s ' = semi - perimeter

⟶ ' a, b and c ' = sides of the Triangle

⟶ s = a + b + c / 2

According to the question :

● For the Triangular park :

• a = 100 m , b = 90 m , c = 110 m
• s = 100 + 90 + 110 / 2 = 150 m

● Area of the Triangular park :

⟹ $\sqrt{s ( s - a ) ( s - b ) ( s + c )}$

⟹ $\sqrt{150 ( 150 - 100 ) ( 150 - 90 ) ( 150 - 110 )}$

⟹ $\sqrt{150 × 50 × 60 × 40}$

⟹ $3000\:\sqrt{2}m^2$

⟹ $0.3\sqrt{2}\:ha$

⟹ 0.4242 ha

To find :

Rate of planting grass = ₹ 34000 { given }

Amount to be paid ➳ 34000 × 0.4242

➳ 14,422.8

So It's Done !!

Answer 2

Answer:

₹14423 ( approx)

Step-by-step explanation:

Using heron's formula

√s(s-a)(s-b)(s-c)

a = 100m

b = 90m

c = 110m

s = P/2

P = 300

s = 300/2 = 150

Now put the values

√150(150-100)(150-90)(150-110)

√150*50*60*40

3000√2m^2= area of the park

(√2=1.414)

1 hectare = 10000m^2

3000√2/10000 = 0.3√2 hectare

0.3√2 = 0.4242

0.4242 * 34000

=14422.8