Question

The base of a triangular field is three times of its altitude. If 6 the cost oflevelling the field at 75 per hectare is 1012.50, find its base and corresponding height.​

Answer 1

Base = 900 metres

Height = 300 metres

Given :-

• The base of a triangular field is three times of its altitude.

• The cost of levelling the field at Rs. 75 per hectare is Rs. 1012.50.

To find :-

• The base and the corresponding height of the triangle.

Solution :-

Let the altitude of the triangular field be

h metres

The base of the filed = 3 × altitude

The base of the field = 3h metres

The cost of levelling the field at Rs. 75 per hectare = Rs. 1012.50

Area of the triangular field

= Total cost of levelling the filed / The cost per 1 hectare

= 1012.50/75

= 13.5 Hectares

Area of the given filed = 13.5 hectares

We know that

1 hectare = 10000 m²

13.5 hectares = 13.5×10000 m²

13.5 hectares = 135000 m²

We know that

Area of a triangle

= (1/2)×base×altitude sq.units

=> (1/2)×3h×h = 135000

=> (1/2)×3h² = 135000

=> 3h² = 135000×2

=> 3h² = 270000

=> h² = 270000/3

=> h² = 90000

=> h = ±√90000

=> h = ±300

Since, height can't be negative.

Therefore, h = 300 metres

The base of the field = 3h metres

= 3(300) = 900 metres

Answer :-

• The base of the triangular field

= 900 metres

• The corresponding height of the triangular field = 300 metres

Used formulae:-

• Area of a triangle = (1/2)×base×altitude sq.units

Answer 2

UNDERSTANDING CONCEPT :-

• Use unitary method to find the area of triangular field by dividing the total cost of cultivating the field by cost of cultivation per hectare. Equate the area obtained with the formula of the area of the triangle. Use the relation between the base and height of the triangular field to solve for the height of the triangular field.

• Area of traingle = 1/2 × b × h b = base of a triangle and h = height of a triangle

SOLUTION :-

Given - Cost of Levelling the field at

Rs 75 per hectare is Rs 1012.50

Also, base of a triangular field is three

times of its altitude

To find - Base & height

Let the attitude of triangle bey then the base will be 3 y

Area of triangle = 1/2 × base × altitude

= 1/2 × 3y × y = 1/2 × 3y² = 3y²/2

Cost of Levelling the at Rs 75 per hectare

= 75/10000 × 3 y² /2 = 1012.50

(1 hectare = 10000 sq.m)

y² = 1012.50 × 2 × 10000 / 75 × 3 = 90,000

y = √90,000 = 300m = height

and base = 3y = 3 × 300 = 900 m

Answer:-

Base is 900m & height is 300m.

ADDITIONAL INFORMATION :-

• may likely make mistakes bydirectly taking an area of triangular field in hectares but that is not the correct way of solving rather all units should be converted into standard units.