Question

the number of square units in the area of a square is greater than or equal to the number of units in the perimeter of the square. which side length of a square provides a counterexample to the given statement? 10 units 6 units 2 units 4 units clear all

Explanation:

Step1: Recall formulas for square

For a square with side length \( s \), area \( A = s^2 \) and perimeter \( P = 4s \). We need to find \( s \) where \( s^2<4s \) (counterexample to \( A\geq P \)).

Step2: Test \( s = 2 \)

Calculate area: \( A = 2^2 = 4 \). Calculate perimeter: \( P = 4\times2 = 8 \). Here, \( 4<8 \), so \( A < P \), which is a counterexample.

(Testing other options: \( s = 4 \): \( A = 16 \), \( P = 16 \) (\( A = P \)); \( s = 6 \): \( A = 36 \), \( P = 24 \) (\( A > P \)); \( s = 10 \): \( A = 100 \), \( P = 40 \) (\( A > P \)).)

Answer:

2 units (the option with "2 units")