Question

A base of a triangular field is three times the altitude. if the cost of cultivating the field at Rs. 200 per hectare is Rs.4800, find its base ( 1 hectare =10,000 sq.meters)​

Answer 1

Answer:

Its base and altitude are 900 m and 300 m respectively.

Step-by-step explanation:

Let the altitude of triangular field be x

We are given that the base of a triangular field is three times its altitude.

So, Base = 3x

Area of triangle =\frac{1}{2} \times base \times Height=\frac{1}{2} \times 3x \times x

2

1

×base×Height=

2

1

×3x×x

The cost of cultivating the field at Rupee 280 per hectare is Rs 3780

Area of field =\frac{3780}{280}=13.5 hectare

280

3780

=13.5hectare

1 hectare = 10000 sq.m.

13.5 hectare = 13.5 \times 10000 =135000 sq.m.

So, \frac{1}{2} \times 3x \times x = 135000

2

1

×3x×x=135000

x^2= \frac{135000 \times 2}{3}x

2

=

3

135000×2

x = \sqrt{\frac{135000 \times 2}{3}}x=

3

135000×2

x =300x=300

Base = 3x =3(300)=900 m

Height = 300 m

Hence its base and altitude are 900 m and 300 m respectively.

#Learn more:

The base of a triangular field is three times its altitude the cost of cultivating the field at 24.60 per hectare is 332.10 find its base and height

Answer 2

Answer:

Area of field =

Rate

TotalCost

=(

24.68

333.18

)=13.5 hectares

=(13.5×10000)m

2

=135000m

2

Altitude =x meters Base =3x meter

2

1

×x×3x=135000

⇒

2

3x

2

=135000

⇒x

2

=

3

135000×2

=90000

x=300

Base =900m Altitude =300m.