Question

the base of a triangular field is three times its height . if the cost of cultivating the field at rs 36.72 per hectare is rs 495.72 find its base and height.

Answer 1

Answer:

9cm

Step-by-step explanation:

let x be the height.

Therefore,3x=base

Cost of cultivating entire field=cost of cultivating 1ha²*area of triangle

495.72=1/2*x*3x*36.72

On simplification

x=3cm

Therefore, base=3x=9cm.

Answer 2

The base and height are 900 m and 300 m respectively.

Step-by-step explanation:

The cost of cultivating the field at rs 36.72 per hectare is rs 495.72

Area of triangular field $= \frac{495.72}{36.72}=13.5 hectares$

1 hectare = 10000 sq.m.

13.5 hectares =$13.5 \times 10000=135000 sq.m.$

Let the height be x

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

Base = 3x

Area of triangular field =$\frac{1}{2} \times Base \times Height = \frac{1}{2} \times 3x \times x$

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

Height = 300 m

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

Hence The base and height are 900 m and 300 m respectively.