Question

Rectangle divided into four rectangles. The perimeters of rectangle #1, #2, #3 #4 are 10 cm, 20 cm, 28 cm and 18 cm respectively. Find the perimeter of big rectangle.

Answer 1

The perimeter of the big rectangle is 38 cm

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