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Question
The base of a triangular field is three times its height. If the cost of cultivating the field at ₹ 36.72 per 100 m2 is ₹ 49,572; find its base and height.
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Solution
Since the cost of cultivating the field at the rate of Rs. 36.72 per 100 square metre is Rs. 49,572.
Area of the triangular field = `(49572 xx 100)/36.72` = 1,35,000 sq. m
Let the height of the triangle be h.
Now,
Area of the triangular field = `1/2` × base × height
1,35,000 = `1/2 xx h xx 3h`
⇒ h2 = 90,000
⇒ h = 300
Height (h) = 300m
Base (3h) = 3 × 300 = 900 m.
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