Question

List the sides of FGH in order from least to greatest if m

Answer 1

We have a triangle FGH

The three angles of the triangle FGH are given as

$\begin{gathered} m\angle F=4x+7 \\ m\angle G=5x-31 \\ m\angle H=7x-52 \end{gathered}$

Recall that the sum of all three angles of a triangle must be equal to 180°

$\begin{gathered} m\angle F+m\angle G+m\angle H=180\degree \\ 4x+7+5x-31+7x-52=180 \\ 16x-76=180 \\ 16x=180+76 \\ 16x=256 \\ x=\frac{256}{16} \\ x=16 \end{gathered}$

Now, we can calculate the exact measure of the angles

$\begin{gathered} m\angle F=4x+7=4(16)+7=64+7=71\degree \\ m\angle G=5x-31=5(16)-31=80-31=49\degree \\ m\angle H=7x-52=7(16)-52=112-52=60\degree \end{gathered}$

Let us draw the triangle FGH

Recall that the side opposite the least angle is the least side and vice versa.

The means that the side opposite the angle G is the least side (FH)

Then the side opposite the angle H is the greater side (FG)

Finally, the side opposite the angle F is the greatest side (GH)

Therefore, the sides of the triangle FGH in order from least to greatest is

FH, FG, GH