# Blog

## Brainteaser: Walkin’ the perimeter

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Difficulty: Tricky

Lavonne is a security guard who has to walk around the outside of an L-shaped building. She knows the length of the longest sides, 200 metres and 140 metres. She also knows the shape of the building and that each of the angles are 90 degrees. Curious to know about how many metres she walked, Lavonne draws the outline of the building:

What is the building’s perimeter?

## Need a hint?

Remember that the perimeter is the sum of all the side lengths of a shape.

There are some lengths on this map that are impossible to work out. But that doesn’t mean you don’t know anything about them!

Can you find two walls that add together to make 200 metres?

Lavonne’s building has a perimeter of 680 metres.

The perimeter is the sum of all the side lengths of a shape. You don’t need to find the exact length of each side, as long as you know what they add up to!

It helps to remember an important rule about rectangles: their angles are all 90 degrees and so their opposite sides are equal. This means that a rectangle’s top side is always equal to the bottom side, and the right side is always equal to the left side.

The unusual building shape can be thought of as a rectangle with a smaller rectangle pushed in or cut out:

It’s easy to find the side lengths of the large rectangle – the opposite sides are the same length, so the unlabelled sides are 200 and 140 metres long.

But looking at the two shorter vertical sides, highlighted in blue, and it’s clear that they also add up to 200 metres. That’s because the hole is a rectangle, so its opposite sides are equal.

We can use the same tactic with the horizontal segments to find that they must add up to 140 metres.

Adding it all up, we get 200 + 140 for the two sides we know, plus 200 + 140 for the pairs of shorter sides. In total, we get a perimeter of 680 metres!

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