Question

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

Answer 1

SOLUTION

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

ratio of sides
12: 17:25

let them be
12x,17x, 25x respectively

perimeter of a triangle = sum of all sides

540 = 12x,17x, 25x
540 = 54x
x = 10

all sides measure
12x = 12×10 = 120
17x = 17× 10 = 170
25x= 25 × 10 = 250

it's semipetimeter = 540/2
= 270

using heron's formula area of the triangle =

root {(s)(s-a)(s-b)(s-c)}
where s is the semipetimeter and a,b,c

area the sides of the triangle.

root {( 270)(270-120)(270-170)(270-250)}

= 9000cm^2.