Identical pieces

You have split figures into rectangles to find their area. Today, we will use identical rectangles to find a missing length. Lin makes this panel from 4 identical rectangles. The panel is 24 centimetres wide. Find the length of each rectangle. Identical rectangles have the same length and the same breadth, even when one is turned. On the right, the turned rectangle stands 1 length tall, and on the left the same height is 3 breadths. We call the breadth of each rectangle 1 unit. The length of each rectangle is 3 units. Across the top, we have the length of a flat rectangle and the breadth of the turned one. 3 units plus 1 unit make 4 units. Those 4 units measure 24 centimetres. So the panel is 4 units wide. So 1 unit is 24 divided by 4, which is 6 centimetres. 3 times 6 centimetres is 18 centimetres. The length is 3 units, so 3 times 6 is 18 centimetres. When pieces are identical, look for the same side measured two ways.

Lin makes this panel from 3 identical rectangles. The panel is 21 centimetres wide. Find the length of each rectangle. Try it first. Pause if you like. Identical rectangles have the same length and the same breadth, even when one is turned. On the right, the turned rectangle stands 1 length tall, and on the left the same height is 2 breadths. We call the breadth of each rectangle 1 unit. The length of each rectangle is 2 units. Across the top, we have the length of a flat rectangle and the breadth of the turned one. 2 units plus 1 unit make 3 units. Those 3 units measure 21 centimetres. So the panel is 3 units wide. So 1 unit is 21 divided by 3, which is 7 centimetres. 2 times 7 centimetres is 14 centimetres. The length is 2 units, so 2 times 7 is 14 centimetres.

Lin makes this panel from 5 identical rectangles. The panel is 40 centimetres wide. Find the length of each rectangle. Try it first. Pause if you like. Identical rectangles have the same length and the same breadth, even when one is turned. On the left, the turned rectangle stands 1 length tall, and on the right the same height is 4 breadths. We call the breadth of each rectangle 1 unit. The length of each rectangle is 4 units. Across the top, we have the length of a flat rectangle and the breadth of the turned one. 4 units plus 1 unit make 5 units. Those 5 units measure 40 centimetres. So the panel is 5 units wide. So 1 unit is 40 divided by 5, which is 8 centimetres. 4 times 8 centimetres is 32 centimetres. The length is 4 units, so 4 times 8 is 32 centimetres. Identical rectangles have equal lengths and equal breadths. Find a side you can measure two ways.