Question

the perimeter of a triangle is 300m. is its side are in a ratio 3:5:7. find the area of the triangle

Answer 1

3x+5x+7x=300

15x=300

x=20

By using cosine rule to find some angle from the triangle.

let a =3x b=5x c=7x

a=60 b=100 c=140(We need to find the angle between a and b)

c^2=a^2+b^2-2ab cos C ( Find the angle opposite of line c)

19600=3600+10000-[ 2(60)(100) cosC]

-6000= 12000cos C

C=120

By using formula of Side angle side

(ab sin C)/2=(60x100 sin120)/2

=2598.07m^2

Answer 2

Hey

Let triangle ABC

AB=3x ,BC=5x ,AC=7x

perimeter=300m


AB +BC+AC =300

3x+5x+7x=300

15x=300

x=300/15

x=20

therefore,
AB=3x=3(20)=60m
BC=5x=5(20)=100m
AC=7x=7(20)=140m

S=a+b+c/2
S=300/2
S=150m

area=√s(s-a)(s-b)(s-c)

area=√150(150-60)(150-100)(150-140)

area=√150*90*50*10

area=√3*2*3*5*5*2*3*3*5*2*5*5*2*5

area=2*2*3*5*5*5*√3

area=1500√3m²

I hope its help you
mark branilest