Answer:
Area = 144 units^{2}
Step-by-step explanation:
Since the sides of a square are equal, the perimeter is:
[tex]perimeter = 4*length[/tex]
Substituting perimeter = 48 and [tex]length = 5x+2[/tex], then:
[tex] 48 = 4*(5x+2)[/tex]
By dividing on both sides:
[tex]\frac{48}{4} = \frac{4*(5x+2)}{4}[/tex]
[tex] 12 = 5x+2 [/tex]
Rearranging:
[tex] 12 -2 = 5x+2-2 [/tex]
[tex] 10 = 5x [/tex]
[tex] x = 2 [/tex]
To calculate the area, we need to calculate the length:
[tex]length = 5x+2 = 5*2+2 = 12[/tex]
The formula for Area is:
[tex]Area = Length^{2}[/tex]
[tex] Area = 12^{2} = 144 units^{2} [/tex]
