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The area of a square is always greater than its perimeter. Which of the following side-lengths for a square provides a counterexample that disproves the statement above?A. 2TT.B. 4.C. 7.5.D. 10.E. 125.

Sagot :

MrRoyal

Answer:

a. 2

Step-by-step explanation:

Area of a square is calculated as:

[tex]Area = Length * Length[/tex]

And the perimeter is

[tex]Perimeter = 4 * Length[/tex]

For (a):

[tex]Length = 2[/tex]

[tex]Area = 2 * 2 = 4[/tex]

[tex]Perimeter = 4 * 2 = 8[/tex]

For(b):

[tex]Length = 4[/tex]

[tex]Area = 4 * 4 = 16[/tex]

[tex]Perimeter = 4 * 4 = 16[/tex]

For (c):

[tex]Length=7.5[/tex]

[tex]Area = 7.5 * 7.5-56.25[/tex]

[tex]Perimeter = 4 * 7.5 = 30,[/tex]

For (d):

[tex]Length = 10[/tex]

[tex]Area = 10 * 10 = 100[/tex]

[tex]Perimeter = 4 * 10 = 40[/tex]

For (e):

[tex]Length = 125[/tex]

[tex]Area = 125 * 125 =15625[/tex]

[tex]Perimeter = 4 * 125 = 500[/tex]

From (a) to (e), only side length 2 has a higher perimeter.

Hence, it disproves the statement

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