Question

Fill in the Blank.

Difference of any two sides of a triangle is ___ than the third side.

Answer 1

Sum and difference of the sides of a triangle:

According to the triangle inequality theorem, the total of lengths of any two triangle sides must be greater than the third side.

For a triangle ABC,

$AB+BC>AC$

Suppose $AB=3,BC=4,AC=5$.

$$\begin{gathered} \Rightarrow 3+4>5 \\ \Rightarrow 7>5 \end{gathered}$$

If the difference of AB and BC is taken,

$$\begin{gathered} AB-BC \\ =4-3 \\ =1<5 \\ =<AC \end{gathered}$$

Hence, the difference of any two sides of a triangle is less than the third side.