The perimeter of a triangular field is 540m and its sides are in the ratio 25:17:12. Find the area of the field. Also, find the cost of ploughing the field at Rs 5 per m2.
Answers
Let the height of the parallelogram be h.
Area of a parallelogram =base×height
=24×h
=24h
Semi-Perimeter of triangle with sides 10 cm, 24 cm and 26 cm is,
=
2
a+b+c
=
2
10+24+26
=
2
60
=30 cm
Now by using heron's formula,
Area of triangle =
30(30−10)(30−24)(30−26)
=
30×20×6×4
=
6×5×5×4×4×6
=6×5×4
=120 sq. cm
But it is given that area of the parallelogram is equal to the area to triangle,
24h=120
⇒h=5 cm
Hence, the height of the parallelogram is equal to 5 cm.
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Answer:
Area of the triangular field is 9000m² and cost of ploughing the field is ₹45000.
Step-by-step explanation:
We have,
Ratio of sides = 25 : 17 : 12
Then let the sides be,
25x, 17x and 12x
But, given
Perimeter = 540m
Then,
Perimeter = 25x + 17x + 12x
540m = 54x
x = 540/54
x = 10
Then,
Sides are
25x = 25(10) = 250m
17x = 17(10) = 170m
12x = 12(10) = 120m
Now, we can find the Area using Heron's formula,
Area = √[s(s - a)(s - b)(s - c)]
But,
s = Perimeter/2
s = 540/2
s = 270 m
Then,
Let a = 250m
b = 170m
c = 120m
So,
Area = √[(270)(270 - 250)(270 - 170)(270 - 120]
Area = √[270 × 20 × 100 × 150]
Area = √(3³ × 10 × 2 × 10 × 10² × 3 × 5 × 10)
Area = √(3⁴ × 2 × 10⁵ × 5)
Area = √(3⁴ × 2 × (2 × 5)⁵ × 5)
Area = √(3⁴ × 2 × 2⁵ × 5⁵ × 5)
Area = √(2⁶ × 3⁴ × 5⁶)
Area = 2³ × 3² × 5³
Area = 8 × 9 × 125
Area = 9000m²
Now, we find find the cost,
We know that,
Cost = Rate × Area
So,
Rate = ₹ 5/m²
Area = 9000m²
Thus,
Cost = 5 × 9000
Cost = ₹45000
Hence,
Area of the triangular field is 9000m² and cost of ploughing the field is ₹45000.
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