Question

find area of triangle whose perimeter is 180 cm and two of its sides are of length are 80 cm and 18 cm. also calculate the altitude of triangle corresponding to shortest sides

Answer 1

Perimeter =180
So third side is 180-80-18=82
Let a=80 b=18 c=82
So s=(a+b+c)/2
=90
s-a=10
s-b=72
s-c=8
Area of triangle
=
$\sqrt[]{s(s - a)(s - b)(s - c)}$
$\sqrt{90 \times 10 \times 72 \times 8}$
$2 \times 3 \times 5 \times 2 \times 2 \times 2 \times 3$
720cm²
Now let altitude of triangle with the smallest side be x
So area of triangle =720
1/2(18)(x)=720
x=80cm