Question

the base of a triangular field is three times its height.If the xost of cultivating the field at RS. 36 per hectare is RS. 486,find its base and height (1 hectare = 10000 m²).

Answer 1

heya,

area of triangle = 1/2×base×height.
1/2*x*3x
= 3/2x²

1 hectare = 10,000 sq. meter

the rate of cultivating the field = rs. 36 
total cost = rs. 486.

total cost = area of the triangular field × rs. 36
3/2x² × 36/10,000 = 486.
x² = $\frac{486}{36} * \frac{2}{3} * 10000$
x² = 90000 m²
x = 300 m

height of the triangular field = x = 300 m
base of the triangle field = 3x = 3*300 = 900m

thank you.
 

Answer 2

Let the altitude of the triangle be x.

Then the base of the triangular field is 3x.

We know that Area of the triangle = 1/2 * b * h

                                                         = 1/2 * 3x * x

                                                         = 3x^2/2.


Given that the cost of cultivating the field at 36 per hectare = 36 * 3x^2/2

                                                                                                     = 54x^2/2.


54x^2 = 486

x^2 = 486/54

x^2 = 9 * 10000

x = 300

if the altitude is 300 then the base is 3 * 300 = 900.


Therefore the base = 900m.

                  the height = 300m.


Hope this helps!