Question

2 The base of a triangular field is three times its altitude. If the cost of
sowing the field at Rs 58 per hectare is Rs 783, find its base and height​

Answer 1

Answer:

base= 9 and altitude=3

Step-by-step explanation:

Let the altitude of the triangle be y

Then the base will be 3y

Area of triangle is 1/2 x base x altitude

                          =1/2 x 3y x y

                          = 1/2 x

                          = /2

                       

Cost of sowing the field at rs 58 per hectare = 58 × 3x2/2 = 87x2

Therefore, 87x2 = 783

= 783/87 = 9

⇒ y = 3

Base = 3(3) = 9

Hence base is 9 and altitude is 3.

Answer 2

Given :-

The base of a triangular field = 3 × Altitude

The cost of  sowing the field at Rs. 58 per hectare = Rs. 783

To Find :-

The base of the triangular field.

The height of the triangular field.

Solution :-

We know that,

• b = Base
• h = Height
• a = Height

According to the question,

Area of triangular field = Cost of sewing field/ Rate of sowing

Substituting their values,

= 783/58

= 13.5 hectare

By converting,

1 hectare = 10000 m²

13.5 hectare = 135000 m²

Therefore,

Area of triangular field = 135000 m²

Let altitude of triangular field be 'x'.

By the formula,

$\underline{\boxed{\sf Area \ of \ triangle=\dfrac{1}{2} \times Breadth \times Height}}$

Substituting their values,

3/2 x² × 58/10000 = 783

x² = 783/58 × 2/3 × 10000

x = √90000

x = 300

Height = 300

Base = 3x

= 300 × 3 = 900

Therefore, the base and the height are 900 m and 300 m respectively.