Answer:
a). radius if each quarter circle = 3.5 cm
b). Perimeter of the shaded part
= 61.98 cm
Explanation:
Let's call the length of the the removed portion x= radius
The ratio of the length of the rectangle to its breadth is 12:5.
Length = 17 + 2x
Breadth = 3+2x
(17+2x)/(3+2x)= 12/5
5(17+2x) = 12(3+2x)
85 + 10x = 36 +24x
85-36 = 24x-10x
49 = 14x
49/14= x
7/2 = x
3.5 = x
Length of the radius if each quarter circle = 3.5 cm
The length is now equal to
17 + 2x = 17 + 2(3.5)
= 17 + 7
= 24
The breadth is now equal to
3 +2x = 3+ 2(3.5)
= 3+7
= 10
Perimeter if the whole shape
= 2(length+ breadth)
= 2(24+10)
= 2(34)
= 68
Arc of the quarter circle
= (2πr)/4
= (2*3.14*3.5)/4
= 21.98/4
= 5.495
Perimeter of the shaded part= perimeter of the whole shape +arc of the 4 quarter circle - 8x
Perimeter of the shaded part
= 68+4(5.495) - 8(3.5)
= 68+21.98-28
= 61.98 cm