Question

If the perimeter of a triangle is 34 cm if the second side is twice of the first side and third is two more than second then find all sides of the triangle

Answer 1

The length of sides of triangle are 6.4 cm , 12.8 cm and 14.8 cm

Solution:

Given that perimeter of triangle = 34 cm

The perimeter of a triangle is the sum of the lengths of all its sides.

For a triangle with sides a, b and c, the perimeter P is defined as:

Perimeter = a + b + c

Let "a" be the length of first side and "b" be the length of second side and "c" be the length of third side

Given that,

The second side is twice of the first side

second side = 2(first side)

b = 2a ------ eqn 1

From eqn1,

$a = \frac{b}{2}$   -------- eqn 2

Also given that,

Third side is two more than second side

third side = 2 + second side

c = 2 + b ------ eqn 3

Substitute eqn 2 and eqn 3 in perimeter formula,

$Perimeter = \frac{b}{2} + b + 2 + b\\\\34 = \frac{b + 2b + 4 + 2b}{2}\\\\68 = b + 2b + 4 + 2b\\\\68 = 5b + 4\\\\5b = 64\\\\b = 12.8$

b = 12.8

Thus from eqn 3,

c = 2 + b = 2 + 12.8 = 14.8

c = 14.8

From eqn 2,

$a = \frac{b}{2} = \frac{12.8}{2} = 6.4$

a = 6.4

So the length of sides of triangle are 6.4 cm , 12.8 cm and 14.8 cm