Question

The base of a triangular field is twice its height. If the cost of cultivating the field at Rs 14.50 per 100 m square is Rs 52200 , find its base and altitude

Answer 1

Step-by-step explanation:

Cost of cultivating 100 square m field = Rs 14.50

Hence cost of cultivating 1 square m field =14.50/100 = Rs 0.1450

Let the height of triangular field be x m

Therefore base = 2x m

$Area \: of \: triangular \: field \: = \frac{1}{2} \times base \: \times height \\ = \frac{1}{2} \times 2x \: \times x \\ = {x}^{2} \\ total \: cost \: of \: cultivation \: = cost \: per \: {m}^{2} \times Area \: of \: triangular \: field \: \: \\ 52200 = 0.1450 \times {x}^{2} \: \\ {x}^{2} = \frac{52200}{0.1450} \\ {x}^{2} = 360000 \\ x = 600 \: m \\ 2x \: = 2 \times 600 = 1200 \: m \\ hence \: \\ base \: = 1200 \: m \\ altitude \: = 600 \: m.$