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Question
The altitude and the base of a triangular field are in the ratio 6: 5. If its cost is ₹ 49,57,200 at the rate of ₹ 36,720 per hectare and 1 hectare = 10,000 sq. m, find (in metre) dimensions of the field.
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Solution
Total cost = ₹ 49,57,200
Rate = ₹ 36,720 per hectare
The total area of the triangular field
= `4957200/36720 xx 10000 "m"^2 = 1350000 "m"^2`
The ratio in altitude and base of the field = 6: 5
Let altitude = 6x
and base = 5x
∴ Area = `1/2 "Base" xx "Altitude"`
⇒ 1350000 = `1/2 xx 5x xx 6x`
⇒ `15x^2 = 1350000 ⇒ x^2 = 1350000/15`
⇒ `x^2 = 90000 = (300)^2`
∴ x = 300
∴ Base = 5x = `5 xx 300 = 1500` m
and altitude = `6x = 6 xx 300 = 1800`m
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