Question

Can anyone help with this​

Answer 1

`\boxed{\boxed{\pink{\bf \leadsto Perimeter\ of \ cross\ shaped \ pattern \ is \ 128cm. }}}`

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 :-

`\bf\implies\orange{Area_(square)=(side)^2}\\\\\bf\implies a* a = 64cm^2\:\:\bigg\lgroup \red{\sf Assuming \ side \ to \ be \ a }\bigg\rgroup \\\\\bf\implies a^2 = 64cm^2 \\\\\bf\implies a=√(64cm^2) \\\\\implies\boxed{\purple{\bf a = 8cm }}`

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 ,

`\bf\implies Area_(rec.) = (3)/(2) * Area_(square) \\\\\bf\implies Area_(rec.) = (3)/(2) * 64 cm^2 \\\\\bf\implies \boxed{\red{\bf Area_(rectangle)= 96cm^2}}`

Hence side will be :-

`\bf\implies lenght * breadth = 96cm^2\\\\\bf\implies 8cm * l = 96cm^2\\\\\bf\implies l =(96cm^2)/(8cm)\\\\\bf\implies \boxed{\red{\bf lenght = 12cm }}`

Hence the lenght of rectange is 12cm .

Now , the perimeter of the given figure will be ,

`\bf\implies Perimeter_(cross) = 8(lenght) + 4(breadth) \\\\\bf\implies Perimeter_(cross) = 8* 12cm + 4* 8cm \\\\\bf\implies Perimeter_(cross) = 96cm + 32cm \\\\\bf\implies \boxed{\red{\bf Perimeter_(cross) = 128cm }}`

Hence the perimeter of the given cross is 128cm .