Question

Find the area of a triangle whose perimeter is 180cm and its two sides are 80 cm and 18 cm. Calculate the altitude of triangle corresponding to its shortest side.

Chap:Heron's formula

Answer 1

let the third side be y

perimeter=y+80+18=180

=y+98=180

=y=180-98

=y=82m

by heron's formula we have

$\sqrt{x(x - a)(x - b)(x - c) }$

x=1/2(a+b+c)

=1/2(80+82+18)

=1/2×180

90

$\sqrt{90(90 - 80)(90 - 82)(90 - 18)}$

$\sqrt{90 \times 10 \times 8 \times 72}$

$\sqrt{518400}$

=720m2

so the area is 720m square

the shortest side is 18m

the area=1/2(base×altitude)

720m2=1/2×18×altitude

720m2=9×altitude

altitude=720/9

=80m