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17 votes
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).​

User Heringer
by
5.3k points

1 Answer

11 votes

Answer:

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.

User Zxcat
by
7.0k points
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