If gf is a midsegment of cde, find cd. a. 3.4b. 6.8 c. 13.6 d. 14

C

Step-by-step explanation:

Triangle CGF and triangle CED are similar. Hence, the ratio of their corresponding sides are equal. Thus we can write:

We can now cross multiply and solve for CD:

Since GF is a midsegment of CDE, CD is double of CF. So we can write:

By using quadratic formula and with a=3, b= -5.2, and c= -1.6, we find the value of x to be:

Since the expression for CD is , we plug in into this expression to find value of CD:

The correct answer is C

C. 13.6

Step-by-step explanation:

We have been given that GF is a mid-segment of CDE.

Since we know that mid-segment of a triangle is half the length of its parallel side.

We can see that ED is parallel to GF , so measure of GF will be half the measure of ED. We can represent this information as:

Let us substitute given value of GF and ED to find our x.

Multiply both sides of equation by 2.

We can see that triangle CFG is similar to triangle CDE, so we will use proportions to find length of CD.

Substitute given values.

Upon substituting x=2 in our equation we will get,

Let us simplify our equation.

Therefore, CD equals 13.6 and option C is the correct choice.