Question

the base of a triangular field is three times its altitude. if the cost of cultivating the field at Rupee 280 per hectare is Rs 3780, find its base and altitude

Answer 1

Let height be x.
Base be 3x.
Area=3780/280=13.5hectare=135000m
3x×x/2=135000
x=300
height= 300m
base= 900m

Answer 2

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 =$\frac{1}{2} \times base \times Height=\frac{1}{2} \times 3x \times x$

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

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

1 hectare = 10000 sq.m.

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

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

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

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

$x =300$

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​

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