Question

the perimeter of a triangular plot is 240 M if two of its sides are 78 M and 50 M then find the area of the triangular plot

Answer 1

the area of the triangle is 1680m2.

Answer 2

Perimeter of Triangular plot is 240 m
That is sum of sides of Triangle = 240 m
Consider a = 78 m, b = 50 m, c = ?
Now, a+b+c = 240m
= 78+50+c = 240
128 + c = 240
c = 240/128
c = 112 m
Now Sides of Triangle are
a = 78 m
b = 50 m
c = 112 m
--- To find the area of Triangular Plot we will use Hero's Formula that is
$\sqrt{s(s - a)(s - b)(s - c)} \\ s = \frac{240}{2} \\ s = 120 \\ \sqrt{120(120 - 78)(120 - 50)(120 - 112) } \\ \sqrt{120 \times 42 \times 70 \times8 } \\ \sqrt{2822400} \\ 1680$
So area of triangular plot is 1680m^2