Question

if two sides of a triangle are 8 cm and 16 cm and the perimeter of the triangle is 34 cm , what is the third side ?​

Answer 1

The third side is 10
Perimeter=s1+s2+s3
Perimeter=16+8+s3
34=24+s3
S3=34-24
s3=10

Answer 2

Given :

• Two sides of a triangle :-
• First side = 8 cm
• Second side 16 cm
• Perimeter of the triangle = 34 cm

To find :

• The third side

Knowledge required :-

• Formula of perimeter of triangle :-

⠀Perimeter of triangle = Sum of all sides

~Understanding the concept ::

Here, we are given two sides and the perimeter of the triangle. And we have to find the third side for that firstly, we will assume the third side as x. By adding all the sides and keeping them equal to the perimeter of the triangle, we will find the value of the third side.

Solution

Let the third side of the triangle be x.

Perimeter = Sum of all sides.

⠀⠀⠀⇒ 34 = 8 + 16 + x

⠀⠀⠀⇒ 34 = 24 + x

⠀⠀⠀⇒ 34 - 24 = x

⠀⠀⠀⇒ 10 = x

The value of x = 10

∴ The third side of the triangle = 10 cm

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Let's verify :-

Substitute the value of x in 34 = 8 + 16 + x

Taking Rhs,

⠀⠀⠀⇒ 8 + 16 + x

⠀⠀⠀⇒ 8 + 16 + 10

⠀⠀⠀⇒ 34

Lhs = Rhs

Hence, verified.

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Some related formulae :-

• Area of isosceles triangle = 1/2 × base × height
• Area of equilateral triangle = √3/4 a²
• Heron's formula = √s(s - a)(s - b)(s - c)