Question

Given that two sides of isosceles triangle are of length 7cm and 8cm. Then find the length of third side.
$\begin{align}
  & \text{a) 7cm} \\
 & \text{b) 7cm or 8cm} \\
 & \text{c) 8cm} \\
 & \text{d) None of these}\text{.} \\
\end{align}$

Answer 1

Hint: Now the given triangle is an isosceles triangle and we know that the isosceles triangle is a triangle in which two sides are equal. Hence we will use this condition to find the third side of our triangle

Complete step by step answer:
Now we are given that the triangle is an isosceles triangle and the sides of the triangle are of length 7cm and 8cm.
Now we know an isosceles triangle is a triangle with two sides equal
For example consider the triangle ABC where AB = BC.

Now let us say our required triangle is triangle XYZ. Such that XY = 7cm and YZ = 8cm.
Let us say the length of the third side which is XZ is ‘a’ cm.
Let us draw a figure of such a triangle.

Now for this triangle to be equal we need at least two sides equal.
We know that XY is not equal to YZ.
Hence now we just have two possibilities.
Either it can be XY = XZ or it can be YZ = XZ.
Now since XY = 7cm and YZ = 8cm.
We have XZ = 7cm or XZ = 8cm.
Hence we have the third side of the triangle is 7cm or 8cm.
Option b is the correct option.

Note:
 Note that the condition for the equilateral triangle is that all three sides must be equal. The condition for the isosceles triangle is that two sides must be equal. Now even if all three sides are equal the triangle can be called an isosceles triangle. Hence the equilateral triangle is nothing but a special case of an equilateral triangle.