Question

If the two sides of an isosceles triangle are 3 cm and 8 cm, then the length of the third side is
(a) 2 cm
(b) 8 cm
(c) 3 cm
(d) 1 cm

Answer 1

Hint:In this question, as given that the given triangle is isosceles so it has two equal sides. As given two sides are not equal the third side will be any of these two. Now, we need to check which of these satisfies the condition that the sum of two sides is greater than the third side that will be the result.

Complete step-by-step answer:
TRIANGLE: A triangle is a polygon that consists of three sides, three edges, three vertices and three angles
Isosceles Triangle: A triangle which has two equal sides and the angles opposite to these equal sides as equal angles is called an isosceles triangle.

Triangle Properties:
The sum of the length of two sides of a triangle is greater than the length of the third side.
In the same way, the difference between the length of two sides should be less than the length of the third side.
Now, from the given question we have the two sides of the isosceles triangle as 3 cm, 8 cm
Now, here as the triangle is isosceles so the third side should be equal to any of the given two sides.
Now, let us assume that the third side as 3 cm the we have
\[3+3<8\]
Here, it does not satisfy the property of the triangle and if any one of the three possibilities does not satisfy the property of the triangle it cannot form a triangle.
Thus, the third side cannot be 3 cm
Now, if we consider the third side as 8 cm then we get,
\[3+8>8\]
Here, it satisfies the property of triangle
Thus, the third side is 8 cm
Hence, the correct option is (b).

Note:Instead of using the property that the sum of length of two sides of a triangle is greater than the third side we can also use that the difference of length of two sides of a triangle is less than the third side. Both the methods give the same result.It is important to note that here we cannot use any sine rule or cosine rule of the triangle as we don't know the angles and we don't have specific sides. So, it is suggested to just check the property of triangle first and then think of other higher methods.