Question

the side of a triangular field are 165m,143m and 154m. find the cost of ploughing it at 12 paise per sq. m. ​

Answer 1

Given :

• Sides of a Triangular field are 165m , 143m and 154m.

To Find :

• Cost of ploughing it at 12 paisa per m².

Solution :

• a = 165m
• b = 143m
• c = 154m

$\longmapsto\tt{s=\dfrac{a+b+c}{2}}$

$\longmapsto\tt{s=\dfrac{165+143+154}{2}}$

$\longmapsto\tt{s=\cancel\dfrac{462}{2}}$

$\longmapsto\tt\bold{s=231m.}$

Now ,

$\longmapsto\tt{Area=\sqrt{s(s-a)(s-b)(s-c)}}$

$\longmapsto\tt{\sqrt{231(231-165)(231-143)(231-154)}}$

$\longmapsto\tt{\sqrt{231\times{66}\times{88}\times{77}}}$

$\longmapsto\tt{\sqrt{11\times{7}\times{3}\times{11}\times{3}\times{2}\times{11}\times{2}\times{2}\times{2}\times{11}\times{7}}}$

$\longmapsto\tt{11\times{11}\times{7}\times{3}\times{2}\times{2}}$

$\longmapsto\tt\bold{10164{m}^{2}}$

So , The Area of Triangular Field is 10164 m²

Now ,

Cost of Ploughing at 12 paisa per m² :

$\longmapsto\tt{10164\times{12}}$

$\longmapsto\tt\bold{121968\:paisa}$

In Rupees :

$\longmapsto\tt{\dfrac{121968}{100}}$

$\longmapsto\tt\bold{Rs.1219.68}$