Question 19 • (OC27) MATH COLL ALGEBRA-1200710-S1-Degele-VOL7006P
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
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 height and the base are irrational.
Explanation
A terminating decimal is rational, and a repeating decimal is also rational. The triangle’s area is calculated as A = 1/2 × base × height; multiplying rational numbers, including 1/2, gives a rational result. Therefore, choice C is correct: the formula and the substituted values are rational.
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