The length of the third side can be either 10 or 8, if the lengths of two sides of an isosceles triangle are eight and 10.
According to the given question.
The lengths of two sides of an isosceles triangle are 8 and 10.
Since, the properties of an isosceles triangle are
- Two sides are congruent to each other.
- The sum of the length of the two sides of a triangle is greater than the length of the third side.
- The difference between the two sides of a triangle is less than the length of the third side.
So, according to the property of an isosceles triangle
The third side must be less than the sum of 8 and 10.
⇒ length of third side < 8 + 10
⇒ length of third side < 18
And,
Length of the third side > 10 - 8
⇒ length of the third side > 2
But, the triangle is an isosceles triangle therefore, the third side must be either 8 or 10.
And
8 or 10 both are less than 18 and greater than 2.
Therefore, the length of the third side can be either 10 or 8.
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