Answer:
base = 519.62, height = 173.21 m
Step-by-step explanation:
Let the base and height of the triangle be represented by b and h respectively.
Thus,
b = 3h
Area of a triangle = [tex]\frac{1}{2}[/tex] x base x height
For the given triangle,
area = [tex]\frac{1}{2}[/tex] x b x 3h
= [tex]\frac{3}{2}[/tex]bh
Area of the triangle = [tex]\frac{3}{2}[/tex]bh
To determine the number of hectares,
36 per hectare = 486
hectare = [tex]\frac{486}{36}[/tex]
= 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 = [tex]\frac{3}{2}[/tex]bh
135 000 = [tex]\frac{3}{2}[/tex]bh
270000 = 3bh
bh = [tex]\frac{270000}{3}[/tex]
= 90000
bh = 90000
But, b = 3h
3h x h = 90000
3[tex]h^{2}[/tex] = 90000
[tex]h^{2}[/tex] = [tex]\frac{90000}{3}[/tex]
= 30000
h = [tex]\sqrt{30000}[/tex]
= 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.
