Sam is determining the area of a triangle. In this triangle, the value for the height is a terminating decimal, and the value for the base is a repeating decimal. What can be concluded about the area of this triangle?
a. The area will be irrational because the height is irrational.
b. The area is irrational because the numbers in the formula are irrational and the numbers substituted into the formula are rational.
c. The area is rational because the numbers in the formula are rational and the numbers substituted into the formula are rational.
d. The area will be rational because both the heig

All repeating decimals are still rational because they can be expressed as fractions. For example, \( 0.\overline{4}=\frac49 \).
Terminating decimals are also always rational. If you have a terminating decimal like \( 53.247 \) it can be expressed as \( \frac{53247}{1000} \).

As for the formula for the area of a triangle, it is \( A=\frac12bh \), where b is the base and h is the height. The ½ is obviously rational (it’s a fraction) and the numbers we are substituting into the formula will also be rational, so we will get a rational area as our result as well.

The area has to be rational (we’ve just proved it) so A and B are not possibilities.
C looks correct from what we concluded but I’d still like you to take a look at answer choice D because you didn’t finish typing it.


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