Question

Find the area of a triangle whose perimeter is 180cm and 2 of its sides are 80cm and 18cm. also find the altitude of the triangle corrosponding to the longest side as the base.

Answer 1

Answer:

Perimeter = 180cm

=x+80cm+18cm=180cm

=x=180cm-98cm

=x=82cm

then,

semi perimeter,s=perimeter/2

=180cm/2

=90cm

By Heron's formula,

Area = √[90(90-82)(90-80)(90-18)]

=√(90×8×10×72)

=720cm²

Area = 720cm²

=(1/2)bh=720cm²

=(1/2)×82cm×h=720cm²

=h=(720cm²×2)/82cm

=h=17.56cm

Thus ,

Area =720cm²

altitude =17.56

Answer 2

Answer:

1) Let third side be x

∴ x + 80 + 18 = perimeter = 180

⇒               x = 180 - 98

⇒                x =82cm

2) s= p/2

⇒ s= 180/2 = 90cm

area of triangle = √s(s-a)(s-b)(s-c)                                            [herons formula]

                         = √90(90-80)(90-18)(90-82)

                         =√90(10)(72)(8)

                         =√3(3)(5)(2)(5)(2)(2)(2)(2)(3)(3)(2)(2)(2)            [factorization]

                        = 3(5)(2)(2)(2)(2)(3)

                       =720 cm^{2}

3) area of triangle = (1/2)bh

⇒                720 =  (1/2)82h

⇒                     h = 720/41

⇒                     h = 17.5 cm