Question

The base of triangular field is three times its height. If the cost of cultivating the field at Rs. $36.72$ per $100$ $m^2$ is Rs. $49,572$; find its base and height.

• A. Base $600$ m, height = $300$ m
• B. Base $400$ m, height = $300$ m
• C. Base $800$ m, height = $300$ m
• D. Base $900$ m, height = $300$ m

Answer 1

The correct option is D Base $900$ m, height = $300$ m

Since the cost of cultivating the field at at the rate of Rs. $36.72$ per $100$ square metre
is Rs. $49,572$ => Area of the field $=\frac{49,572\times 100}{36.72}=135000sqm$
Now, area of the triangular field $=\frac{1}{2}\times$ base $\times$ height $=135000$
$=>\frac{1}{2}\times \left(3h\right)\times \left(h\right)=135000$
$=>h^2=90000$
$=>h=300m$
And base $=3\times 300=900m$