Question

cost of fencing a triangular field at Rs.3.50 per m is Rs.245. If two of its

side length are 21m and 29 m respectively, find the length of third side of this

triangle and hence find its area.no​

Answer 1

Solution:

Total cost for fencing triangular field = Rs. 245

Rate of fencing per square metre = Rs. 3.50

We will calculate what is Perimeter of triangular field by the cost required to fence the field and rate of fencing per square metre as fencing is done on boundary of the field.

Perimeter of field  = Total cost/Rate of fencing per square metre

                              = 245/3.50

                              = 70 m

Perimeter of Triangular field = First side + Second Side + Third Side

70 = 21 + 29 + Third Side

70 = 50 + Third Side

Third Side = 70 - 50

Third side = 20 m                                        

To find the area of triangle we will apply Heron's formula.

[We are using Heron's formula as all three sides are unequal and no height is given too]

$Area \ of \ triangle = \sqrt{p(p-a)(p-b)(p - c)}$

whereas,

p = half perimeter = (a + b + c)/2

Let First, Second and Third side of Triangle be a, b, c.

a = 21 m

b = 29 m

c = 20 m

Then,

p = (21 + 29 + 20)/2 = 70/2 = 35 m

$Area \ of \ triangle = \sqrt{p(p-a)(p-b)(p - c)}$

$Area \ of \ triangle = \sqrt{35(35-21)(35-29)(35 - 20)}$

$Area \ of \ triangle = \sqrt{35(14)(6)(15)}$

$Area \ of \ triangle = \sqrt{44100}$

$Area \ of \ triangle = 210 \ sq. \ m$

The area of triangular field is 210 m²(sq. m)