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
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)}
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
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