Question

the perimeter of a triangle is 50 cm.one side is 4 cm longer than smaller side and third side is 6 cm less than twice of smaller side. find area of triangle.

Answer 1

Given,

Let smaller side = a           --------------- (i)
one side = a + 4                 --------------- (ii)
third side = 2a - 6              --------------- (iii)

On solving (i),(ii),(iii) we get

= a + a + 4 + 2a - 6 =50

= 4a - 2 = 50

a = 13

Substituting a value in (i),(ii),(iii)

smaller side = 13

one side = 17

third side = 20

Perimeter  = 20 + 17 + 13/2

                   = 50/2

                   = 25

Area = s(s-a)(s-b)(s-c)^1/2

         = (25(25-13)(25-17)(25-20))^1/2

         = 20(30)^1/2

         = 20 root 30


Hope it helps!

Answer 2

let the second side be x cm.
first side = x+4cm
second side =x cm
third side= 2x-6 cm
we know that perimeter is 50 cm
then
(x+x+4+2x-6) cm = 50
4x-2 =50
4x =50 +2
4x =52
x= 52/4 = 13
so the second side is 13 cm.
first side is 13+4 =17 cm
third side is 13-6= 7 cm
now
the area of triangle is 1/2 *base*height
1/2*13*x. (because we do not know the value of height)
x=2/13cm will be the height
area = 1/2 * 13*2/13 = 1 cm

hope this will helpfull to you