Grades 9-10 Video Solutions 2022-2022_9-10

Video Transcription

Question 16. The diagram shows a large rectangle. A, B, C, D. Divided into 12 identical small rectangles. What is the ratio AD to DC? Let's draw out the  rectangles. Now let's look at one individual rectangle and call one side A and the other side B. And now we can label the sides of this rectangle. One  side will be A plus B plus B. This side will be B plus B plus B. And the bottom side is A plus B plus A plus A. Now since this is a rectangle, we can set the top  and the bottom sides equal to each other. So 3B equals 3A plus B. Subtract B from both sides and get 2B equal to 3A. Dividing both sides by 2, we get B equal  to 1 and a half A. Now to find the ratio, we can ignore the bottom side. And we're trying to find the ratio of AD, which is B plus B plus A, or 2B plus A, to DC,  which is 3B. Like so. And since we know that B is 1 and a half A, we can substitute that. And this gives us A plus 3A to 4.5A, or 4A to 4.5A. And this  ratio, we can get rid of the A's and multiply both by 2. And this will give us a ratio of 8 to 9. And that gives us our answer, which is A, 8 to 9.

Video Summary

The problem involves finding the ratio of AD to DC in a large rectangle, divided into 12 identical smaller rectangles. By defining the smaller rectangle's sides as A and B, the problem sets up equations based on equivalent sides and solves for the relationship between A and B, finding B to be 1.5A. The sides AD and DC are then expressed as combinations of A and B, with AD equaling 2B + A and DC equaling 3B. Substitution and simplification lead to the ratio of 8:9, providing the final answer.