is a rectangle in which cm, and is a square whose side length is cm,
where . Find the length of and the perimeter of the shaded part.
Step 1: Determine the length of .
Write the ratio for , and substitute the length of . Multiply each term of the ratio on the right by 2 to form an equivalent ratio with a numerator of 10.
Then add to find the length of .
Opposite sides of a rectangle are equal in length. So,
Step 2: Find the perimeter of the shaded part by adding the side lengths.
Note that we know the length of because