Pls help The figure below shows a rectangle with its corners removed. Each of the 4 identical comers removed is a quarter circle. The ratio of the length of the rectangle to its breadth is 12:5.
(a) What is the radius of each quarter circle?
(b)What is the perimeter of the shaded part? Take pie = 3.14
Give your answer correct to 1 decimal place.

a). radius if each quarter circle = 3.5 cm

b). Perimeter of the shaded part

= 61.98 cm

Step-by-step 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