Question

which of the following is a counterexample for this conditional statement? if a shape is a rectangle, then its perimeter is an even number. a rectangle with sides measuring 10 and 7 a rectangle with sides measuring 3.9 and 5.1 a rectangle with sides measuring 2.1 and 7.4 a rectangle with sides measuring 1.5 and 2.5

Explanation:

To find a counterexample, we need to check which rectangle has a perimeter that is not an even number. The formula for the perimeter of a rectangle is \( P = 2(l + w) \), where \( l \) is the length and \( w \) is the width.

Step 1: Analyze Option 1 (10 and 7)

Calculate the perimeter: \( P = 2(10 + 7) = 2(17) = 34 \), which is even. So this is not a counterexample.

Step 2: Analyze Option 2 (3.9 and 5.1)

Calculate the perimeter: \( P = 2(3.9 + 5.1) = 2(9) = 18 \), which is even. So this is not a counterexample.

Step 3: Analyze Option 3 (2.1 and 7.4)

Calculate the perimeter: \( P = 2(2.1 + 7.4) = 2(9.5) = 19 \), which is odd (not even). Let's verify the last option to be sure.

Step 4: Analyze Option 4 (1.5 and 2.5)

Calculate the perimeter: \( P = 2(1.5 + 2.5) = 2(4) = 8 \), which is even. So this is not a counterexample.

Answer:

a rectangle with sides measuring 2.1 and 7.4