Question

sides of traingle are in the ratio of 12-17-25 and is perimeter 540cm. Find the area of traingle​

Answer 1

Answer:

12x= 120cm

17x=170cm

25x=250cm

Area of Traingle = 9000$cm^{2}$

Step-by-step explanation:

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 =

√{(s)(s-a)(s-b)(s-c)}

where s is the semipetimeter and a,b,c

area the sides of the triangle.

√{( 270)(270-120)(270-170)(270-250)}

= 9000$cm^{2}$

Answer 2

Step-by-step explanation:

consider 1st side of triangle=12x

2nd side of triangle = 17x

3rd side of triangle = 25x

perimeter of triangle=540cm

perimeter of triangle=sum of all sides

540=12x+17x+25x

540=54x

x=540÷54

x=10

1st side of triangle=12×10=120

2nd side of triangle=17×10=170

3rd side of triangle =25×10=250

s = (a + b + c)/2 = (120 + 170 + 250)/2 = 540/2

= 270 cm

∴Area of triangle = root under (√s(s -a) (s -b)(s -c))

root under (√270(270 - 120)(270 - 170)(270 - 250))

= root under (√270 x 150 x 100 x 20)

= 100 under root(√27 x 15 x 20)

= 100 x 9 x 5 x 2

= 9000 cm2