Categories

# Unclear Perimeter

What is the perimeter of the outer rectangle? All angles shown are right angles.

#### Solution

The perimeter is 28.

The big rectangle can be divided into a left rectangle, a middle square, and a right rectangle. The perimeter can then be written as 6 + 8 + (left+bottom sides of the left rectangle, shown in red) + (right+top sides of the right rectangle, shown in green).

Because the left rectangle is a rectangle, the left+bottom sides are equal to the right+top sides, and you can see from the diagram that these must have a combined length of 6.

Because the right rectangle is a rectangle, the right+top sides are equal to the left+bottom sides, and you can see from the diagram that these must have a combined length of 8.

That means the perimeter is 6 + 8 + 6 + 8 = 28.

With the information provided, you are not able to solve for the side length of the square. However, the perimeter is constant regardless of the side length of the square. You just need to recognize that the line segments above are the same length, which means the perimeter is twice the combined length of the labeled segments.