Question

Suppose you are given the three lengths shown and are asked to construct a triangle whose sides have lengths $r,s,$and $t.$ Can you do so $?$ State the theorem from Chapter $6$ that applies.

Short answer

No, it’s not possible to construct a triangle whose sides have lengths $r,s$ and $t$.

Step-by-step solution

Step 1. Given information.

Three lengths are given.

Step 2. Concept used.

According to triangle inequality theorem,

In a triangle,

the sum of the spans of any two sides is always greater than the span of the third side.

Step 3. Observe the following figure.

Here, from the figure,

it can be observed that $r+s<t$

Therefore, it’s not possible to construct a triangle whose sides have lengths $r,s$ and $t$.