Question

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

Answer 1

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 = $\frac{1}{2}$ x base x height

For the given triangle,

area = $\frac{1}{2}$ x b x 3h

       = $\frac{3}{2}$bh

Area of the triangle = $\frac{3}{2}$bh

To determine the number of hectares,

36 per hectare = 486

hectare = $\frac{486}{36}$

             = 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 = $\frac{3}{2}$bh

135 000 = $\frac{3}{2}$bh

270000 = 3bh

bh = $\frac{270000}{3}$

     = 90000

bh = 90000

But, b = 3h

3h x h = 90000

3$h^{2}$ = 90000

$h^{2}$  = $\frac{90000}{3}$

     = 30000

h = $\sqrt{30000}$

  = 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.