Question

The perimeter of the rectangle ABCD is 30 cm. Three other rectangles are placed so that their centres are at the points A, B, D. The sum of their perimeters is 20 cm. What is the total length of the thick line?

Answer 1

Explanation:

The perimeter of ABCD is 30cm

The Sum of the perimeter of three rectangles at the corner is 20cm.

following the variables as the same as you assigned

large rectangle: u by v

rectangle center A: 2a by 2b

rectangle center B: 2c by 2d

rectangle center D: 2e by 2f

2 equations (from the givens):

2u+2v=30

2(a + b + c + d + e + f )= 20

now to find the length

a+b+a/2+b/2+(v-b/2-d/2)+c/2+d+c+d/2+(u-c/2)+(v-f/2)+e/2+f+e+f/2+(u-e/2-a/2)

which is (a+b+c+d+e+f)+u+v+u+v = 10+30=40