Math, asked by ranameenakshidhiraj, 4 months ago

A triangular park has sides 120m 80m 50m . Find Its Area with herons formula also find the cost of planting grass at the rate of Rs20 per m2. Full explanation

Answers

Answered by kartik2507
1

Step-by-step explanation:

sides of the triangular park are 120m, 80m, 50m

a = 120 b = 80 c = 50

s = (a+b+c)/2

s = (120+80+50)/2

s = 250/2

s = 125

area of triangular park with heron's formula

area = √{s (s-a)(s-b)(s-c)}

 =  \sqrt{s(s - a)(s - b)(s - c)}  \\  =  \sqrt{125(125 - 120)(125 - 80)(125 - 50)}  \\  =  \sqrt{125 \times 5 \times 45 \times 75}  \\  =   \sqrt{ {5}^{3}  \times 5 \times 5 \times  {3}^{2} \times  {5}^{2} \times 3  }  \\  =  \sqrt{ {5}^{3 + 1 + 1 + 2}  \times  {3}^{2 + 1} }  \\  =  \sqrt{ {5}^{7}  \times  {3}^{3} }  \\  =   {5}^{3}  \times 3 \times  \sqrt{5 \times 3}   \\ = 125 \times 3 \times  \sqrt{15}  \\  = 375 \sqrt{15}

area of the triangular park = 375√15 sq m

cost of planting grass = Rs. 20 per metre

total cost of planting grass = 20 × 375√15

= 7500√15

= 7500 × 3.87

= 29025

the total cost of planting grass = Rs. 20,025

Hope you get your answer

Answered by akshattrana
0

Step-by-step explanation:

sides of the triangular park are 120m, 80m, 50m

a = 120 b = 80 c = 50

s = (a+b+c)/2

s = (120+80+50)/2

s = 250/2

s = 125

area of triangular park with heron's formula

area = √{s (s-a)(s-b)(s-c)}

\begin{gathered} = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{125(125 - 120)(125 - 80)(125 - 50)} \\ = \sqrt{125 \times 5 \times 45 \times 75} \\ = \sqrt{ {5}^{3} \times 5 \times 5 \times {3}^{2} \times {5}^{2} \times 3 } \\ = \sqrt{ {5}^{3 + 1 + 1 + 2} \times {3}^{2 + 1} } \\ = \sqrt{ {5}^{7} \times {3}^{3} } \\ = {5}^{3} \times 3 \times \sqrt{5 \times 3} \\ = 125 \times 3 \times \sqrt{15} \\ = 375 \sqrt{15} \end{gathered}

=

s(s−a)(s−b)(s−c)

=

125(125−120)(125−80)(125−50)

=

125×5×45×75

=

5

3

×5×5×3

2

×5

2

×3

=

5

3+1+1+2

×3

2+1

=

5

7

×3

3

=5

3

×3×

5×3

=125×3×

15

=375

15

area of the triangular park = 375√15 sq m

cost of planting grass = Rs. 20 per metre

total cost of planting grass = 20 × 375√15

= 7500√15

= 7500 × 3.87

= 29025

the total cost of planting grass = Rs. 20,025

Hope you get your answer

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