Question

If EF = FG, DE = 2t, and DG = t + 30, what is the value of t?

A. t = 10

B. t = 15

C. t = 20

D. t = 25

Answer 1

The value of t is found by setting up and solving the equation 2t + t = t + 30, which simplifies to 3t = t + 30. The correct value for t is 15.

Step-by-step explanation:

The student is trying to figure out the value of t in the context of a geometric problem, where the lengths of line segments DE, EF, FG, and DG are related algebraically. Given the equations DE = 2t, EF = FG, and DG = t + 30, we can find t by setting up an equation.

Since EF = FG and DE + EF = DG, then DE + FG = DG. Substituting the given values, we have 2t + (t) = t + 30. By simplifying this equation, we get 2t + t = t + 30 which reduces to 3t = t + 30.

Solving for t:
3t - t = 30
t = 15

Therefore, the correct answer is B. t = 15.