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 3.2 and 5.3 a rectangle with sides measuring 3.9 and 5.1 a equilateral triangle with sides measuring 7 a circle with radius of 8

Explanation:

Step1: Recall perimeter formula for rectangle

The perimeter formula of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.

Step2: Calculate perimeter of first rectangle

For a rectangle with sides $l = 3.2$ and $w = 5.3$, $P=2(3.2 + 5.3)=2\times8.5 = 17$, which is odd. This is a counter - example as it is a rectangle with an odd perimeter.

Step3: Analyze other options

The third option is an equilateral triangle, not a rectangle. The fourth option is a circle, not a rectangle. For a rectangle with sides $l = 3.9$ and $w = 5.1$, $P = 2(3.9+5.1)=2\times9 = 18$ (an even number), so it is not a counter - example.

Answer:

a rectangle with sides measuring 3.2 and 5.3