Question

In the diagram below of triangle CDE, F is a midpoint of CD and G is a midpointof DE. If FG = 9x – 59, and CE = 34 – x, what is the measure of CE?

Answer 1

Step-by-step explanation:

As the figure is an equilateral triangle, that is, it has three equal sides, the equation of the midpoint also corresponds to half the measure of the side CE.

Therefore we must formulate a single equation that allows us to find the value of the variable x and find the measure of CE.

the exercise is as follows:(First we find value of x)

`\begin{gathered} CE=34-x\text{ }FG=9x-59 \\ (34-x)=(9x-59) \\ 34+59=9x+x \\ 93=10x \\ (93)/(10)=x \\ 9.3=x \end{gathered}`

Now we must replace the value of the variable x found in the equation to find the measure of CE;

`\begin{gathered} CE=34-x; \\ CE=(34-9.3) \\ CE=24.7 \\ \text{ANSWER: The measure of the CE is 24.7} \end{gathered}`