Question

Two sides of an isosceles triangle measure $5cmand13cm.$ What is the possible values of third side?

Answer 1

Calculating the possible values of third side:

Using the properties of the sides of an isosceles triangle, we know that “The length of two sides of an isosceles triangle are always equal.”

By the triangle inequality theorem, we know that “Sum of any two sides of triangle should be greater than the third side”.

Case (i) : If we take the length of equal sides as $5cm$, then

$5\mathrm{cm}+5\mathrm{cm}=10\mathrm{cm}<13\mathrm{cm}(\mathrm{lesser}\mathrm{than}\mathrm{the}\mathrm{third}\mathrm{side})$, not satisfying the triangle inequality.

Case (ii) : If we take the length of equal sides as $13cm$, then

$13\mathrm{cm}+13\mathrm{cm}=26\mathrm{cm}>5\mathrm{cm}(\mathrm{greater}\mathrm{than}\mathrm{the}\mathrm{third}\mathrm{side})$, satisfying the the triangle inequality.

Final Answer: Hence, the possible value of the length of third side for isosceles triangle is $13cm$.