Question

The base of a triangular field is 2.4 times its height. If the cost of levelling the field at the field at the rate of Rs. 20 per square metre is Rs. 9,600; find its base and height.

• A. base$=$ $12$ cm and height $=$ $20$ cm
• B. base$=$ $48$ cm and height $=$ $20$ cm
• C. base$=$ $42$ cm and height $=$ $20$ cm
• D. base$=$ $16$ cm and height $=$ $20$ cm

Answer 1

Answer: (B)

base$=$ $48$ cm and height $=$ $20$ cm

Since the cost of levelling the field at the rate of Rs. $20$ per square metre is Rs. $9,600$
=> Area of the field $=\frac{9600}{20}=480sqm$
Now, area of the triangular field $=\frac{1}{2}\times base\times height=480$
$=>\frac{1}{2}\times \left(2.4h\right)\times \left(h\right)=480$
$=>h^2=400$
$=>h=20m$
And base $=2.4\times 20=48m$