The base of a triangular field is three times its height. If the cost of cultivating the field at rupees 36.72 per 100 m square is rupees 49572 find base and height
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Let the base of triangle = b
height of triangle = h
we are given that b = 3h
Rate of cultivation = ₹36.72 per 100m^2 = 36.72/100 = ₹0.3672 per m^2
Total cost = ₹49572
area of field = 49572 ÷ 0.3672 = 135000 m^2
Thus area of triangular field = 135000
or 1/2 × bh = 135000
or 1/2 × 3h × h = 135000
or 3/2 h^2 = 135000
or h^2 = 135000×2/3 = 90000
or h = √90000 = 300m
b = 3h = 3×300 = 900m
Hence, base of field is 900m and height is 300m.
height of triangle = h
we are given that b = 3h
Rate of cultivation = ₹36.72 per 100m^2 = 36.72/100 = ₹0.3672 per m^2
Total cost = ₹49572
area of field = 49572 ÷ 0.3672 = 135000 m^2
Thus area of triangular field = 135000
or 1/2 × bh = 135000
or 1/2 × 3h × h = 135000
or 3/2 h^2 = 135000
or h^2 = 135000×2/3 = 90000
or h = √90000 = 300m
b = 3h = 3×300 = 900m
Hence, base of field is 900m and height is 300m.
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