Question

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?

Answer 1

Answer:

The area is rational because the numbers in the formula are rational.

Step-by-step explanation:

All repeating decimals are still rational because they can be expressed as fractions. For example,

$\frac{1}{7}=0.\overline{142857} \end{document}$

So every recurring decimal must be a fraction.

Also every terminating decimal can be represented as a fraction.

0.25  =  $\frac{1}{4}$

So  the area is rational because the numbers are rational.

Area = $\frac{1}{2}$ X Base X Height

Base is Rational and Height is Rational. Hence Area=Rational.

When these rational numbers are substituted into the formula,the area must be rational.