the base of a triangular plot is three times its height. The cost of cutting the grass of the plot at rupees 540 per hectare is rupees 7290, find the base and height
Answers
Answer:
Base of the triangular park = 900 m
And, Height of the triangular park = 300 m
Step-by-step explanation:
Given:
Cost of cutting the grass of the plot = Rs. 7290 at Rs. 540 per hectare.
Finding the Base and Height:
Area of the triangular park = 7290/540 hectare
= 27/2 hectare
=[ (27 × 10000) / 2 ] m² [∵One hectare = 10000 m².]
= 135000 m²
Let the base and height of the triangular park is b metre and h metre respectively.
Given that, base of the triangular plot is three times its height,
∴ b = 3h
∵Area of the triangle = 1/2 × b × h unit²
∴Area of the triangular plot = 1/2 × b × h
⇒135000 = 1/2 × 3h × h [∵b= 3h & Area = 135000 m²]
⇒270000 = 3 h²
⇒ h² = 270000/3
⇒ h² = 90000
⇒ h = √90000
⇒ h = 300 m
∴b = 3 × 300 m [∵b = 3h]
⇒ b = 900 m
∴Base and height of the triangular plot is 900 m and 300 m.
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