The base of a triangular field is three times its height. if the cost of cultivating the field at rupees 46. 72 per metre square is rupees 2522.88, find its base and height.
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Total Cost of cultivating = ₹2522.88
Rate of cultivating = ₹46.72/m²
So, area = Cost/Rate
→ area = 2522.88/46.72
→ area = 54 m²
Now, given that base is three times of its height. So, if height is h, base is 3h
We know that area of triangle = 1/2 × base × height
→ 1/2 × 3h × h = 54
→ 3h²/2 = 54
Cross multiply,
3h² = 54 × 2
→ 3h² = 108
→ h² = 108/3
→ h² = 36
→ h = √36
→ h = 6 m
So, base = 3h = 3 × 6 = 18 m
Answer :- Base is 18 and height is 6 m.
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Solution:-
Let the Height of the Triangular Field be "x" m.
=> Base of the Triangular Field = 3x m.
Now,
Area of Triangular Field = 1/2 × Base × Height
=> 1/2 × x × 3x
=> 3x^2 /2
Given that Cost of Cultivating the Field is 2522.88 Rupee.
Cost of 1m^2 = 46.72
=> Cost of 3x^2/2 m^2 = 46.72 × 3x^2/2
=> 2522.88 = 46.72 × 3x^2/2
Hence,
Height of Triangular Field = "x" = 6 m.
& Base of Triangular Field = 3x = 18m.
Let the Height of the Triangular Field be "x" m.
=> Base of the Triangular Field = 3x m.
Now,
Area of Triangular Field = 1/2 × Base × Height
=> 1/2 × x × 3x
=> 3x^2 /2
Given that Cost of Cultivating the Field is 2522.88 Rupee.
Cost of 1m^2 = 46.72
=> Cost of 3x^2/2 m^2 = 46.72 × 3x^2/2
=> 2522.88 = 46.72 × 3x^2/2
Hence,
Height of Triangular Field = "x" = 6 m.
& Base of Triangular Field = 3x = 18m.
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