Question

For the following figure, name the longest and the shortest side of the triangle.

Short answer

The longest side is $GI$and the shortest side is$GH$.

Step-by-step solution

Step 1. Apply the concept of angles.

From the properties of the triangle, that side opposite to the greater angle is greater and the side opposite to the smaller angle is smaller.

The Sum of all sides of a triangle equals to 180 degrees.

Step 2. Check the figure.

Consider the figure $\Delta GHI$.

Step 3. Find the angle.

From the figure, the measure of angles are as follows:

$$\begin{gathered} \angle G={32}^{\circ } \\ \angle H={121}^{\circ } \end{gathered}$$

From angle sum property in a triangle, find the third angle as follows:

$$\begin{gathered} \angle G+\angle H+\angle I={180}^{\circ } \\ {32}^{\circ }+\angle I+{121}^{\circ }={180}^{\circ } \\ \angle B={180}^{\circ }-{153}^{\circ } \\ \angle B={27}^{\circ } \end{gathered}$$

Step 4. Step description.

From the properties of the triangle, that side opposite to the greater angle is greater and the side opposite to the smaller angle is smaller.

Then the greater angle is $\angle H$and the side opposite to $\angle H$is $GI$and the smaller angle is $\angle I$and the side opposite to $\angle I$is $GH$.

Therefore, the longest side is $GI$and the shortest side is $GH$.