Answer :
(a) The two unknown sides of the land are: 85 m, 75 m.
(b) The cost for leveling at Rs. 1420 per kattha is: Rs. 6745600.00.
(c) Total amount received: Rs. 6745600.00.
(d) He made a profit of: 49.01%.
To solve this problem step by step, we will tackle each part of the question:
(a) Find the two unknown sides of the land.
Given:
- Shortest side = 40 m
- Perimeter = 200 m
- Ratio of the other two sides = 17:15
- Let the lengths of the other two sides be 17x and 15x.
- The perimeter is given by the sum of all sides:
40 + 17x + 15x = 200
40 + 32x = 200
32x = 200 - 40
32x = 160
x = 160/32 = 5
- Hence, the lengths of the other two sides are:
17x = 17 × 5 = 85 m
15x = 15 × 5 = 75 m
- So, the sides are 40 m, 85 m, and 75 m.
(b) Calculate the cost for leveling at Rs. 1420 per kattha.
- First, we need to find the area of the triangular land using Heron’s formula.
- The semi-perimeter (s) is given by:
[tex]s = \frac{Perimeter}{2} = \frac{200}{2} = 100[/tex]
- Now calculating the area (A):
[tex]A = \sqrt{s(s-a)(s-b)(s-c)}[/tex]
- Where a = 40 m, b = 85 m, and c = 75 m.
[tex]A = \sqrt{100(100-40)(100-85)(100-75)}[/tex]
[tex]A = \sqrt{100(60)(15)(25)} = \sqrt{2250000} = 1500 \, m^2[/tex]
- To convert the area into katthas:
[tex]Area_{kattha} = \frac{1500}{338.63} \approx 4.43 \, kattha[/tex]
- Cost for leveling:
[tex]Cost = 4.43 \, kattha \times 1420 = Rs. 6290.00[/tex]
(c) If he sold it for Rs. 15,20,000 per kattha, the total amount he received
- Total revenue from selling the land:
[tex]Total\, Amount = 4.43 \, kattha \times 1520000 = Rs. 6745600.00[/tex]
(d) What percent profit did he make?
- Profit = Selling Price - Cost Price
[tex]Profit = 6745600 - 4500000 = Rs. 2245600.00[/tex]
- Percentage Profit:
[tex]Percent\, Profit = \left( \frac{Profit}{Cost\, Price} \right) \times 100 = \left( \frac{2245600}{4500000} \right) \times 100 \approx 49.01\%[/tex]
