Problem number four states. Six rectangles are arranged as shown. The top left-hand rectangle has a height of six centimeters. The numbers within the rectangles indicate their areas in centimeters squared. What is the height of the bottom right-hand rectangle? So let's take our group of rectangles and give the unknown lengths variable lengths. We'll use the letters A through F. Now let's create equations to represent the areas of each of the rectangles in terms of these variables. First let's start out with the rectangle of area 18. The area of a rectangle is its base multiplied by its height, so 18 equals 6 times A. With this we can solve for A by dividing both sides by 6, so we get that A equals 3. Now we can substitute that in, and now let's consider the rectangle with area 12. We know the equation for this rectangle is going to be its base times its height. We know its base and its height is going to be B, so 12 equals 3 times B. Dividing by 3 on both sides, we get that B equals 4. Now let's consider this rectangle here with area 16. We know that the area of it is going to be its base times its height, so it's going to be 4 times C. Dividing both sides by 4, we get that C equals 4. Now let's consider this rectangle with area 32. We know that its base is going to be 4, and then its length is going to be 6 plus D. So dividing both sides by 4 and then subtracting by 6, we get that D equals 2. Now let's consider E here. We can solve for E since we know that E is composed of lengths 6 and 2, so E is going to be equal to 8. Now let's consider the rectangle with an area of 48. So the base is 8 and the height is F. Dividing both sides by 8, we get that F is 6. Let's consider the last rectangle with area 30. Again base times height, so we have 6 times our mystery number. Divide both sides by 6, and we get that the number in question is equal to 5. So the question asked us, what is the height of the bottom right hand rectangle? The answer is 5 centimeters. Letter B.

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