Question

Find the area of the triangle whose perimeter is 180 cm and twoof its sides are of length 80cm and 18cm. Also calculate the altitude of the tiangle corresponding to the shortest side

Answer 1

Let the third side be x

Perimeter of triangle=Sum of its sides

180=80+18+x

180-98=x

x=82 cm

Let a=80cm b=18cm and c=82cm

s=a+b+c/2

=80+18+82/2

=180/2

=90cm

From heron's formula

Area of triangle=√s(s-a)(s-b)(s-c)

=√90(90-80)(90-18)(90-82)

=√90*10*72*8

=√9*10*10*9*8*8

=9*10*8

=720cm^2

Area of trangle=1/2 x b x h

720=1/2*18*h (since the shortest side is 0f 18cm)

720=9h

720/9=h

80cm=h