2 The base of a triangular field is three times its altitude. If the c

1.	2 The base of a triangular field is three times its altitude. If the cost ofsowing the field at Rs 58 per hectare is Rs 783, find its base and height
Answer» 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.

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

Answer»

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.