Question

The ratio of the base to the altitude of a triangular field is 4:1. If the cost of harvesting the field at Rs 20 per square metre is Rs 4000. Find it Base and Height

Answer 1

$\text{Given :}\\</p><p>\text{ratio of b to h} = \frac{4}{1}\\</p><p>\text{Since the cost of harvesting is} \: 20 m^{-2} \\</p><p>\implies \text{Area of field} = \frac{\text{total cost}}{\text{cost of harvesting per metre sq.}} = \frac{4000}{20} = 200 m^2\\</p><p></p><p>\text{we know the formula of area for a triangle} = \frac{1}{2} \times b \times h \\</p><p>\implies 200 = \frac{1}{2} \times b \times h\\</p><p>\implies 400 = b \times h\\</p><p>\implies 400 = 4h \times h (\frac{b}{h} = {4}{1}\: \text{or} \: b = 4h)\\ \implies h^2 = 100\\</p><p>\implies h = 10 m \\</p><p>\text{So, base will be} = 4h = 40 m \\ \\ </p><p>\text{Base and height are 40m and 10m respectively.}</p><p></p><p>$