Question

A large rectangle is made by joining 3 identical small rectangles

the perimeter of 1 small rectangle is 21cm
the width of 1 small rectangle is xcm

work out the perimeter of the larger rectangle

Answer 1

Since three identical small rectangles are joined to form a large rectangle, the large rectangle will have three times the length and the width of a small rectangle.

Let's assume the width of one small rectangle is x cm. Therefore, the length of one small rectangle will be 21 cm - 2x cm (since two widths are subtracted from the total perimeter).

The perimeter of one small rectangle is given by:

Perimeter = 2 * (length + width)

Perimeter = 2 * ((21 - 2x) + x)

Perimeter = 2 * (21 - x)

Perimeter = 42 - 2x

Since the large rectangle is formed by joining three identical small rectangles, the perimeter of the large rectangle will be three times the perimeter of one small rectangle.

Perimeter of the larger rectangle = 3 * (42 - 2x)

Perimeter of the larger rectangle = 126 - 6x

Therefore, the perimeter of the larger rectangle is 126 - 6x cm.