# Problem of the Week Problem B Mystery Dimensions

Eight congruent rectangles are arranged to form a larger rectangle as shown.

1. If the congruent rectangles each have a length of $$6$$ cm and a width of $$3$$ cm, what is the perimeter of the larger rectangle?

2. Suppose that the congruent rectangles each have a longer side of length $$L$$ cm and a shorter side of length $$4$$ cm. Suppose also that the perimeter of the larger rectangle is $$64$$ cm.

1. What is the value of $$L$$?

2. What is the area of one of the eight congruent rectangles?

Extension: Can you solve part (b) without knowing that the length of the shorter side of each rectangle is $$4$$ cm? If so, how?

Themes: Algebra, Geometry & Measurement