Question

The base of a triangular field is three times its height. If the cost of cultivating the field at Rs 1080 per hectare is Rs 14580, find its base and height.

Answer 1

Total cost of cultivating the field = Rs. 14580

Rate of cultivating the field = Rs. 1080 per hectare

Area of the field = $\left(\frac{\mathrm{Total}\mathrm{cost}}{\mathrm{Rate}\mathrm{per}\mathrm{hectare}}\right)$ hectare
= $\left(\frac{14580}{1080}\right)$ hectare
= 13.5 hectare
= (13.5 $\times$ 10000) m² = 135000 m² [since 1 hectare = 10000 m² ]
Let the height of the field be x m.
Then, its base will be 3x m.
Area of the field = $\left(\frac{1}{2}\times 3x\times x\right)$ m² = $\left(\frac{3x^2}{2}\right)$ m²
∴ $\left(\frac{3x^2}{2}\right)$ = 135000
⇒ $x^2=\left(135000\times \frac{2}{3}\right)=90000$
⇒ x = $\sqrt{90000}$ = 300
∴ Base = (3 $\times$ 300) = 900 m
Height = 300 m