Question

the area of a triangle is 154 cm square and its sides are in the ratio 3:4:5 find its perimeter​

Answer 1

Step-by-step explanation:

Let the sides of the triangle be 3xcm,4xcm and 5x cm Then

s=

2

3x+4x+5x

=

2

12x

=6x

∴ Area of Δ=

s(s−a)(s−b)(s−c)

=

6x(6x−3)(6x−4x)(6x−5x)

=

6x×3x×2x×x=6x

2

Given 6x

2

=216⇒x

2

=

6

216

=36⇒x=6

∴ The sides of the triangle are (3×6)cm,(4×6) cm and (5×6) cm i.e 18 cm,24 cm and 30 cm

Perimeter of the Δ =18cm+24cm+30cm

= 72 cm