the sides of triangular field are 200cm 150cm and 120cm. find the cost of ploughing the field at 50 paise per square cm

Answer :

Q.10. We have sides of triangular field  =  200 cm  , 150 cm and 120 cm

Now we find area of triangular field by using Heron's formula  .

We know Heron's formula :

Area of triangle  = $\sqrt{s\left(s -a\right)\left(s -b\right)\left(s -c\right)}$

Here s  = $\frac{a + b + c}{2}$ and a  =   200  b  = 150  and  c = 120 

So ,

s  = $\frac{200 + 150 + 120}{2} = \frac{470}{2} = \mathbf{235}\mathbf{ }\mathit{c}\mathit{m}$
Then
Area of triangular field   = $\sqrt{235\left(235 -200\right)\left(235 -150\right)\left(235 -120\right)} = \sqrt{235 \times 35 \times 85 \times 115} = \sqrt{80399375} = 8966.569 \approx \mathbf{8966}\mathbf{.}\mathbf{57}\mathbf{ }\mathit{c}{\mathit{m}}^{\mathbf{2}}$

Rate of ploughing the field at 50 paise per square cm .

So,

Cost of ploughing the field  =  50 $\times$ 8966.57 = 448328.5 paise  = 4483.285 = Rs .4483.30                               (  Ans )