Question

question 1 - 5. a statement is given below. 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 4 units 2 units 6 units

Explanation:

Step1: Recall formulas

Let the side - length of the square be $s$. The area of the square $A = s^{2}$ and the perimeter $P=4s$.

Step2: Test side - length 2 units

If $s = 2$ units, then $A=s^{2}=2^{2}=4$ square units and $P = 4s=4\times2 = 8$ units. Here, $A

Step3: Test side - length 4 units

If $s = 4$ units, then $A=s^{2}=4^{2}=16$ square units and $P = 4s=4\times4 = 16$ units. Here, $A = P$.

Step4: Test side - length 6 units

If $s = 6$ units, then $A=s^{2}=6^{2}=36$ square units and $P = 4s=4\times6 = 24$ units. Here, $A>P$.

Step5: Test side - length 10 units

If $s = 10$ units, then $A=s^{2}=10^{2}=100$ square units and $P = 4s=4\times10 = 40$ units. Here, $A>P$. But we are looking for a counter - example (where the statement is false), and the side - length of 2 units gives $A

Answer:

2 units