# Question Video: Using Algebraic Expressions to Describe a Perimeter Mathematics • 7th Grade

A square of side 3 cm has a square of side 6π₯ cm cut from one corner as shown in the diagram. Write, in its simplest form, an expression for the perimeter of the remaining shape.

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### Video Transcript

A square of side three centimetres has a square of side six π₯ 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 weβ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 π₯ centimetres square cut out from them. And that means they are three minus six π₯ centimetres long.

And the two sides in the corner both measure six π₯ 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 π₯ centimetres plus six π₯ centimetres plus six π₯ centimetres plus three minus six π₯ centimetres.

Notice that in two places, we have minus six π₯ centimetres and then plus six π₯ centimetres. They cancel each other out. And weβ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.