Answered

the area of a rectangle with a whole number dimensions is 42 square meters.
The least possible perimeter of the rectangle is ___ meters
The greatest possible perimeter of the rectangle is ___ meters

Answer :

MrRoyal

Answer:

The least value of perimeter is:

[tex]Perimeter = 26m[/tex]

The greatest value is:

[tex]Perimeter = 86m[/tex]

Step-by-step explanation:

Given

Shape: Rectangle

[tex]Area = 42m^2[/tex]

Required

Determine the least and greatest possible Perimeters

Area is calculated as:

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

So; first, we need to determine the factors of the given Area;

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

[tex]1 * 42 = 42[/tex]

[tex]2 * 21 = 42[/tex]

[tex]3 * 14 = 42[/tex]

[tex]6 * 7 = 42[/tex]

Perimeter is then calculated as:

[tex]Perimeter = 2 * (Length + Width)[/tex]

When Area is:

[tex]1 * 42 = 42[/tex]

[tex]Perimeter = 2 * (1 + 42)[/tex]

[tex]Perimeter = 2 * 43[/tex]

[tex]Perimeter = 86m[/tex]

When Area is:

[tex]2 * 21 = 42[/tex]

[tex]Perimeter = 2 * (2 + 21)[/tex]

[tex]Perimeter = 2 * 23[/tex]

[tex]Perimeter = 46m[/tex]

When Area is:

[tex]3 * 14 = 42[/tex]

[tex]Perimeter = 2 * (3 + 14)[/tex]

[tex]Perimeter = 2 * 17[/tex]

[tex]Perimeter = 34[/tex]

When Area is:

[tex]6 * 7 = 42[/tex]

[tex]Perimeter = 2 * (6 + 7)[/tex]

[tex]Perimeter = 2 * 13[/tex]

[tex]Perimeter = 26m[/tex]

Comparing the above.

The least value of perimeter is:

[tex]Perimeter = 26m[/tex]

The greatest value is:

[tex]Perimeter = 86m[/tex]

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