Are there any values of x for which the areas of the figures are the same? Explain.

[tex] \dfrac{1}{2}\cdot(x+1)\cdot 2=x\cdot 1\\\\
x+1=x\\\\
0=1 [/tex]
Therefore, there aren't any.
Let's assume that there is a value (or values) of x for which the areas of these two figures aer the same:
Triangle Rectangle
A = (1/2)(2)(x + 1) = (x)(1)
Simplifying,
x + 1 = x
This becomes: 1 = 0
This is never true, regardless of what x is chosen.