Answered

If triangle is isosceles and perimeter is 250 and each two side 100 then find the area of triangle by using herons formula

Answer :

Adithya1234
Perimeter=sum of 3 sides=250 cm
let x be =3rd side 
100+100+x=250
x=50

semi perimeter=250/2=125
heron's formula=√s(s-a)(s-b)(s-c)=area of triangle
=√125(25)(25)(75)
=625√15 unit
consider u as units
Each two side=100 u.
Perimeter=250 u.
Since the first two sides are equal,
Third side =250 u -100*2 u=50 u
Semi perimeter=Perimeter/2
=250 u/2=125 u
Heron's formula:Area=√s(s-a)(s-b)(s-c)
Where a,b and c are 3 sides and s= semi perimeter
=√125*(125-100)*(125-100)*(125-50)
=√125*25*25*75
=√5^8*5*3
=√5^8*15
=5^4√15
=625√15
I COULD HAVE DONE IT WITH PYTHAGORAS THEOREM,
BUT I THINK THIS HERON'S FORMULA CAN BE APPLIED ONLY ON SCALENE TRIANGLES.

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