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What can be concluded about the area of a triangle if the height is a terminating decimal and the base is a repeating decimal? 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.

User Johni
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The area of a triangle is calculated by the formula 1/2 * base * height.

In this case, it is given that the height is a terminating decimal and the base is a repeating decimal. Both terminating and repeating decimals are examples of rational numbers.

A rational number is any number that can be expressed as the quotient or fraction a/b of two integers, with the denominator b not equal to zero.

Therefore, in our triangle, both the base and the height are rational numbers.

The arithmetic multiplication of two rational numbers is also a rational number. This principle applies to our case as the base and the height, which are both rational, are being multiplied to calculate the area.

The number 1/2 in the formula of the area of the triangle is also a rational number.

Therefore, when we multiply the height with the base and with the 1/2 factor, the result is a rational number. This is because the multiplication of any quantity of rational numbers will remain rational.

As a consequence, we can conclude that the area of the triangle is a rational number.

Hence, the statement C) "The area is rational because the numbers in the formula are rational and the numbers substituted into the formula are rational" is the correct choice.

User Sajjan Gurung
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