Question 18. A rectangular strip of paper with dimensions 4 by 13 is folded as shown in the diagram. Two rectangles are formed with areas P and Q, where P equals 2Q. What is the value of X? If we take a closer look at the diagram, we can label these sides as 4, since that is given in the problem. Next, we can label this unknown side as Y. Now since we know that P is equal to 2Q, the areas of the two rectangles, we can make a formula like this. 4 times X is equal to 2 times 4 times Y. If we simplify this, we get X is equal to 2Y. So this means that the length of X is twice as long as Y. Now since this was folded with a right angle, we know that the length of this side will be 4. With this knowledge, if it is unfolded, the length is X plus 4 plus Y, which is equal to 13. If we subtract 4 from both sides, we get X plus Y equal to 9. Now since we know that X is equal to 2Y, we can simplify this and make it X plus half of a Y equal to 9, or 1.5X equals 9. When we divide 9 by 1.5, we get our solution, C, 6.

rectangular strip

folded paper

area ratio

geometry problem

solution steps