A square of side three centimetres has a square of side
six [six 𝑥] centimetres cut from one corner as shown in the diagram. Write, in its simplest form, an expression for the perimeter of the remaining shape.
The perimeter is the distance around a two-dimensional shape. There are six sides in this shape and we need to add the length of all six of these sides. Since we’re dealing with a square, the side on the left is also equal to three centimetres. However, the other two sides have had a six 𝑥 centimetres square cut out from them. And that means they are three minus six 𝑥 centimetres long.
And the two sides in the corner both measure six 𝑥 centimetres because they were part of the square that was taken out. From here, we just need to add all six of these sides: three centimetres plus three centimetres plus three minus six 𝑥 centimetres plus six 𝑥 centimetres plus six 𝑥 centimetres plus three minus six 𝑥 centimetres.
Notice that in two places, we have minus six 𝑥 centimetres and then plus six 𝑥 centimetres. They cancel each other out. And we’re left with three plus three plus three plus three, which equals 12 centimetres.
The distance around this shape written in simplest form is 12 centimetres.