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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.
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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