Question

The length of two sides of an isosceles triangle or 5?and 9 the length of the third side could be

Answer 1

Given:

The lengths of two sides of an isosceles triangle are 5 and 9.

The objective is to find the length of third side.

Since we are given an isosceles triangle then the third side can be either 5 or 9 and it must satisfy the inequality given below, that is:

`|a-b|Where a, b and c are the sides of triangle.<p>Now according to the question, let a= 9 and b=5</p><p></p><p><strong>Case 1: c = 5</strong></p><p>Substitute this in the inequality, we get:</p>[tex]\begin{gathered} |9-5|<5<|9+5| \\ 4<5<14 \end{gathered}`

This is true so c can be 5.

Case 2: c = 9

Substitute this in the inequality, we have:

`\begin{gathered} |9-5|<9<|9+5| \\ 4<9<14 \end{gathered}`

This is also true for c= 9

Hence, the third side can be either 5 or 9.

Thus, option A is true.