Question

6. The base of a triangular field is three times its height. If the cost of cultivating the field

at 36 per hectare is? 486, find its base and height (1 hectare = 10000 m²).​

Answer 1

base = 519.62, height = 173.21 m

Explanation:

Let the base and height of the triangle be represented by b and h respectively.

Thus,

b = 3h

Area of a triangle =
`(1)/(2)` x base x height

For the given triangle,

area =
`(1)/(2)` x b x 3h

=
`(3)/(2)`bh

Area of the triangle =
`(3)/(2)`bh

To determine the number of hectares,

36 per hectare = 486

hectare =
`(486)/(36)`

= 13.5

numbers of hectares = 13.5

Area of the hectares = number of hectares x 10 000 m²

= 13.5 x 10 000

= 135000

Total area of the hectares = 135 000 m²

So that,

area of the hectares = area of the triangle

area of the triangle =
`(3)/(2)`bh

135 000 =
`(3)/(2)`bh

270000 = 3bh

bh =
`(270000)/(3)`

= 90000

bh = 90000

But, b = 3h

3h x h = 90000

3
`h^(2)` = 90000

`h^(2)` =
`(90000)/(3)`

= 30000

h =
`√(30000)`

= 173.2051

h = 173.21 m

So that,

b = 3 x 173.2051

= 519.6153

b = 519.62

Therefore, the base of the triangle is 519.62 m, while the height is 173.21 m.