Let x be side of square.
Area of square = x²
Side of square garden 1: [tex]x _{1} [/tex]
Side of square garden 2: [tex]x _{2} [/tex]
Side of square garden 1, given its area of 1134 cm²
[tex] (x_{1}) ^{2} = 1134cm ^{2} [/tex]
[tex] \sqrt{ (x_{1} }) ^{2} = \sqrt{1134cm ^{2} } [/tex]
[tex] x_{1} = \sqrt{(81)(14)cm^{2} } [/tex]
[tex] x_{1} = 9 \sqrt{14} [/tex] cm
Side of square garden 2, given its area of 3150 cm²
[tex]( x_{2} ) ^{2} =3150 cm ^{2} [/tex]
[tex] \sqrt{( x_{2} ) ^{2} } = \sqrt{3150 cm ^{2} } [/tex]
[tex] x_{2} = \sqrt{(225)(14) cm ^{2} } [/tex]
[tex] x_{2} = 15 \sqrt{14} [/tex] cm
Combined sides (each side) = [tex]9 \sqrt{14} cm + 15 \sqrt{14} cm[/tex]
= 24 [tex] \sqrt{14} [/tex] cms.
Combined Perimeters:
Perimeter of Square = 4x
Perimeters (P) of the two square garden = [tex]4(x _{1} ) + 4( x_{2} )[/tex]
[tex]P _{1} +P _{2} = 4(9 \sqrt{14} cm)+4(15 \sqrt{14} cm)[/tex]
[tex]P _{1} +P _{2} = 36 \sqrt{14} cm + 60 \sqrt{14} cm[/tex]
[tex]P _{1} +P _{2} = 96 \sqrt{14} [/tex] cm
Combined Perimeters of the 2 Square gardens = [tex]96 \sqrt{14} [/tex] cm
