Question

the perimeter of a triangle is 50cm.One side of the triangle is 4cm longer than the smallest side and third side is 6cm less than twice the smallest side.Find the area of the triangle.

Answer 1

Define x:

Let the smallest side be x

2nd side = x + 4

3rd side = 2x - 6

The perimeter is 50 cm:

x + (x + 4) + (2x - 6) = 50

x + x + 4 + 2x - 6 = 50

4x - 2 =50

4x = 52

x = 13 cm

Find the sides:

Side 1 = x = 13 cm

Side 2 = x + 4 = 13 + 4 = 17 cm

Side 3 = 2x - 6 = 2(13) - 6 = 20 cm

Find the area:

area = √p(p-a)(p-b)(p-c)

p = 50 ÷ 2 = 25

area = √25(25 - 13)(25 - 17) (25 - 20)

area = √25(12)(8)(5)

area = √12000

area = 20√30 or ≈ 110 cm²

Answer 2

#AlexaRousey here!!

Perimeter = 50cm,

Let the smallest side be x.

Then one side = x+4,
Other side = 2x-6

=) x + x +4 + 2x - 6 = 50

=) 4x - 2 = 50

=) 4x = 50+2

=) 4x = 52

=) x = 52/4

=) x = 13

Other side = 13+4 = 17cm,
One more side = 2(13) - 6

= 26-6 = 20cm.

Area of triangle by herons formula

= under root [s(s-a) (s-b) (s-c]

If a = 13, b= 17 nd c = 20

=) s = p/2 = 25cm.

A = under root [25(25-13)(25-17)(25-20)]

= under root [25(12) (8)(5)]

= under root 12000

= 20 root30 cm^2

Hope it helps!!