CEMC Banner

Problem of the Week
Problem B
Mystery Dimensions

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

The larger rectangle is made up of three horizontal strips. The top strip consists of two congruent rectangles placed horizontally (with their longer sides horizontal) end to end. The middle strip consists of four rectangles with one rectangle placed vertically followed by two rectangles placed horizontally, one on top of the other, and then another rectangle placed vertically. The bottom strip consists of two rectangles placed horizontally end to end.

  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