Question

If two sides of an isosceles triangle are 4 cm and 10 cm then the length of the third side is__

• A. 10 cm
• B. 4 cm
• C. None of these
• D. 4 cm or 10 cm

Answer 1

Answer: (A)

Two sides of an isosceles triangle are $4$ cm and $10$ cm

In an isosceles triangle two sides are equal.

Case 1:

Let the third side be $4$ cm.

For any triangle with sides let say $a,b,c$, then

$a+b>c$ and

$c+b>a$ and

$c+a>b$

In this case $4+4=8<10$

So, the third side of $4$ cm will not possible.

Case 2:

Let third side be $10$ cm

$10+4=14>10$ and

$10+10=20>10$

Therefore, $10$ cm is the third side.

Hence, the length of the third side is $10$ cm.