Answer:
[tex]\boxed{\boxed{\pink{\bf \leadsto Perimeter\ of \ cross\ shaped \ pattern \ is \ 128cm. }}} [/tex]
Step-by-step explanation:
Given that a cross shaped pattern is made by arranging four identical rectangles around the side of the square . The area of square is 64cm².
So , let's find the side of the square :-
[tex]\bf\implies\orange{Area_{square}=(side)^2}\\\\\bf\implies a\times a = 64cm^2\:\:\bigg\lgroup \red{\sf Assuming \ side \ to \ be \ a }\bigg\rgroup \\\\\bf\implies a^2 = 64cm^2 \\\\\bf\implies a=\sqrt{64cm^2} \\\\\implies\boxed{\purple{\bf a = 8cm }}[/tex]
Hence the side of square is 8cm .
Now , breadth of rectangle will be 8cm.
Now its given that the area of rectangle is 1½ times the area of square. So ,
[tex]\bf\implies Area_{rec.} = \dfrac{3}{2} \times Area_{square} \\\\\bf\implies Area_{rec.} = \dfrac{3}{2} \times 64 cm^2 \\\\\bf\implies \boxed{\red{\bf Area_{rectangle}= 96cm^2}}[/tex]
Hence side will be :-
[tex]\bf\implies lenght \times breadth = 96cm^2\\\\\bf\implies 8cm \times l = 96cm^2\\\\\bf\implies l =\dfrac{96cm^2}{8cm}\\\\\bf\implies \boxed{\red{\bf lenght = 12cm }}[/tex]
Hence the lenght of rectange is 12cm .
Now , the perimeter of the given figure will be ,
[tex]\bf\implies Perimeter_{cross} = 8(lenght) + 4(breadth) \\\\\bf\implies Perimeter_{cross} = 8\times 12cm + 4\times 8cm \\\\\bf\implies Perimeter_{cross} = 96cm + 32cm \\\\\bf\implies \boxed{\red{\bf Perimeter_{cross} = 128cm }}[/tex]
Hence the perimeter of the given cross is 128cm .
