Question

the base of triangular field is three times it's altitude. if the cost of sowing the field at rupees 58 per hectare is rupees 783, find its base and height​

Answer 1

Given :-

Base of the triangular field = 3 × Altitude

The cost of sowing the field at rupees 58 per hectare = Rs. 783

To Find :-

The base of the triangular field.

The height of the triangular field.

Solution :-

We know that,

• l = Length
• h = Height
• b = Base

According to the question,

Take x and the height and 3x as the base of the triangular field

$\underline{\boxed{\sf Area \ of \ triangle = \dfrac{1}{2} \times b \times h}}$

By substituting the values,

$\sf Area \ of \ triangle = \dfrac{1}{2} \times x \times 3x$

So we get,

$\sf Area \ of \ triangle = \dfrac{3}{2} \ x^{2}$

1 hectare = 1000 sq. metre

Given that,

Cost of sowing the field per hectare = ₹ 58

Total rate of sowing the field = ₹ 783

So we can find the total cost by,

Total cost = Area of the field × ₹ 58

By substituting the values,

$\sf \dfrac{3}{2} \ x^{2} \times \dfrac{58}{10000} =783$

By cross multiplication,

$\sf x^{2}=\dfrac{783}{58}\times \dfrac{2}{3} \times 10000$

On further calculation,

$\sf x^{2} = 90000$

By taking the square root,

$\sf x=\sqrt{90000}$

So we get,

$\sf x = 300 \ m$

$\sf Base = 3 \times 300 = 900 \ m$

Therefore, base = 900 m and height = 300 m.