Question

The base of a triangular field is 3 times its height. If the cost of cultivating the field at ₹2800 per hectare is ₹37800, find its base and height.

Answer 1

this is the answer.

hope this helps!

Answer 2

Given:

Base of triangular field=3 times its height

Cost of cultivating=₹37800.

To Find:

Base and height of triangular field.

Solution:

Total cost of cultivating the field=₹37800.

Rate of cultivating the field=₹2800 per hectare.

Area of the field=$(\dfrac{total cost}{rate per hectare})hectares.$

$=(\dfrac{37800}{2800})hectares.$

$=(\dfrac{27}{2})hectares$

=$(\dfrac{27}{2}\times10000)m^{2}$

=$135000m^{2}$

Let the height of the field be x m.

Then its base = 3x m

Area of the field=$(\dfrac{1}{2}\times 3x\times x)m^{2}=(\dfrac{3x^{2}}{2})m^{2}.$

Therefore$,\dfrac{3x^{2}}{2}=135000$

⇒$x^{2}=(135000\times\dfrac{2}{3})=90000$

⇒$x=\sqrt{90000}=300.$

Therefore,base=$(3\times300})$m=900m

height=300m

Hence, the base and height of triangular field is 900 m and 300 m respectively.