Answer:
The perimeter of the big rectangle is 38 cm
Step-by-step explanation:
Rectangle 1 and rectangle 2 share the same width, let their width be a cm while Rectangle 3 and rectangle 4 share the same width, let their width be b cm
Rectangle 1 and rectangle 3 share the same length, let their length be x cm while Rectangle 2 and rectangle 4 share the same length, let their length be y cm
The perimeter of a rectangle = 2(length + breadth).
For rectangle 1:
Perimeter = 2(a + x) = 10
a + x = 5 1)
For rectangle 2:
Perimeter = 2(a + y) = 20
a + y = 10 2)
For rectangle 3:
Perimeter = 2(b + x) = 28
b + x = 14 3)
For rectangle 4:
Perimeter = 2(b + y) = 18
b + y = 9 4)
Adding equations 1, 2, 3 and 4 gives:
a + x + a + y + b + x + b + y = 5 + 10 + 14 + 9
a + a + b + b + x + x + y + y =38
2a + 2b + 2x + 2y = 38
2((a + b) + (x + y)) = 38
For the big rectangle, let its width = c = a + b and its length be d = x + y
The perimeter of the big rectangle = 2 (c + d)
Therefore:
2((a + b) + (x + y)) = 38
2(c + d) = 38 cm = The perimeter of the big rectangle
The perimeter of the big rectangle is 38 cm
