Question

side of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. find its area

Answer 1

hello dude

Ratio of the sides of the triangle = 12 : 17 : 25Let the common ratio be x then sides are 12x, 17x and 25xPerimeter of the triangle = 540cm12x + 17x + 25x = 540 cm⇒ 54x = 540cm⇒ x = 10Sides of triangle are,12x = 12 × 10 = 120cm17x = 17 × 10 = 170cm25x = 25 × 10 = 250cmSemi perimeter of triangle(s) = 540/2 = 270cmUsing heron's formula,Area of the triangle = √s (s-a) (s-b) (s-c)                                       = √270(270 - 120) (270 - 170) (270 - 250)cm2                                       = √270 × 150 × 100 × 20 cm2                                       = 9000 cm2

Answer 2

let the ratio between them will be x
12:17:25 = 12x + 17x + 25x
12x + 17x + 25x = 540
54x = 540
x = 540/54
x= 10
so,
12x = 12× 10 = 120
17x= 17×10= 170
25x= 25×10=250
hence, the sides of triangle are 120cm, 170cm, 250cm
now area of triangle = =√s(s-a)(s-b)(s-c)
=√540×420×370×290
=√81000000
=9000cm square