Step 1: Find the length of .
To find the length of the , subtract the length of from the length of .
Since is parallel to and is parallel to , which is parallel to ,
then is a rectangle with opposite sides of equal length.
Step 2: Find the length of . Use Pythagoras' theorem.
Step 3: Find the perimeter of .
Since , therefore and is a right-angled triangle.
and are vertical angles, so they are equal in measure.
Two right-angled triangles are similar to each other if an acute angle in one triangle is equal to the measure of an acute angle in the other. Therefore,
is similar to .
Since the triangles are similar, the ratio between their perimeters is equal to the ratio between the lengths of two corresponding sides. Therefore,