In the figure below, triangle ADE is an equilateral triangle. If DC=AE+BE and AC=3 inches, what is the length of AB?a. 2.5b. 2c. 1.5d. 1e. None of these.
There might possibly be a better way to solve it, but here is one approach.
Let's let AE = x, and BE = y.
AE + EB = AB (Segment Addition Postulate)
DC = AE +BE
So, by substitution, we get
AE + EB = DC and x + y = AB (substitution)
So, AC = AD + DC (Segment Addition Postulate)
and then, AC = x + x + y, or 3 = 2x + y
Then, we can plug in numbers for x and see what works.
If x = 2.5, then we get 3 = 5 + y and y would have to be negative which is not possible with a shape.
If x = 2, then we get 3 = 4 +y and again we would have a negative number for y which is not possible.
If x = 1.5, then we get 3 = 3 + y and y would have to be 0 which is not possible in a triangle.
If x = 1, then we get 3 = 2 + y so y would be 1. As long as it is OK to have x and y be equal to the same number, then the answer is 1.