Question

The sides of a triangular field are 165 cm, 143 cm and 154 cm. Find the cost of ploughing it at 12 paise per sq. m.

Answer 1

s=a+b+c/2

s=165+143+154/2=231

a=231[231-165] [231-143] [231-154]        {keep it inside the root}

=231[66] [88] [77]          {keep it inside root}

=10164 root 2

Answer 2

Given,

Sides of triangular field = 165 cm, 143 cm and 154 cm.

The cost of ploughing= 12 paise per sq. m

To Find,

The total cost of ploughing the field =?

Solution,

The three sides of the triangular field are 165 cm, 143 cm, and 154 cm.

By herons formula,

the semi perimeter of the triangle  =  s = (a + b + c)/2

Where a, b, and c are the sides of the triangular field

s = (165 + 143 + 154)/2

s = 462/2

s = 231

The area of the triangle according to heron's formula,

$Area = \sqrt{s(s - a)(s - b)(s - c)} \\Area = \sqrt{231(231 - 165)(231 - 143)(231 - 154)} \\Area = \sqrt{231(66)(88)(77)} \\Area = \sqrt{231(66)(88)(77)} \\Area = 10164 cm^2$

Area = 10164 / 10000

Area = 1.0164 $m^2$

Area = 1 $m^2$

The cost of ploughing 1 sq m = 12 paise

The cost of ploughing triangular field = 1.0164 * 12 paise

The cost of ploughing a triangular field = 12.1968 paise

Hence, the cost of ploughing a triangular field is 12.2 paise