Answer:
Perimeter = 14Sqrt2 + 6Sqrt3 units
[tex]14\sqrt{2} + 6\sqrt{3}[/tex][tex]units^{2}[/tex]
Area = 21Sqrt6 units^2
[tex]21\sqrt{6}[/tex][tex]units^{2}[/tex]
Step-by-step explanation:
Perimeter = (2 * Length) = (2 * Width)
Area = Length * Width
Length = Sqrt18 + Sqrt32
Width = Sqrt27
Simplify Square Roots:
- Square the square root to make it a rational (whole) number.
- Find a pair of factors, where one is a square number.
- Square root the factors.
Sqrt18^2 = 18 = 2 * 9 = Sqrt(2*9) =Sqrt2 * 3 = 3Sqrt2
Sqrt32 = 32 =2 * 16 = Sqrt(2 * 16) = Sqrt2 * 4 = 4Sqrt2
Sqrt27 = 27 = 3 * 9 = Sqrt(3*9) = Q3 * 3 = 3Sqrt3
Length = 3Sqrt2 + 4Sqrt2 = 7Sqrt2
Width = 3Sqrt3
Perimeter = (2 * 7Sqrt2) + (2 * 3Sqrt3) = 14Sqrt2 + 6Sqrt3 units
Area = 7Sqrt2 * 3Sqrt3 = (7 * 3) (Sqrt2 * Sqrt3) = 21Sqrt6 units^2
