Two shaded identical rectangular decorative tiles are first placed (one each) at the top and at the base of a door frame for a hobbit’s house, as shown in Figure 1. The distance from W to H is 45 inches. Then the same two tiles are rearranged at the top and at the base of the door frame, as shown in Figure 2. The distance from Y to Z is 37 inches. What is the height of the door frame?
To find the height of the door frame, we need to determine the length of the shaded rectangular decorative tiles. Let's label the length of each tile as "x".
In Figure 1, we can see that the distance from W to H is 45 inches. Since one tile is placed at the top, and another at the base, the total length of both tiles is equal to 45 inches. Therefore, we can write the equation:
x + x = 45
Simplifying this equation, we find:
2x = 45
Now, let's move on to Figure 2. The distance from Y to Z is 37 inches. In this arrangement, both tiles are placed side by side horizontally. So, the combined width of each tile is equal to the distance from Y to Z, which is 37 inches. Thus, we can write the equation:
2x = 37
Now, we have a system of two equations:
2x = 45 (from Figure 1)
2x = 37 (from Figure 2)
To solve this system, we can equate the two expressions for 2x:
2x = 45 = 37
45 = 37
Since these two expressions are contradictory (45 cannot be equal to 37), it means that there was an error in the question or in one of the given measurements. Please double-check the provided information and equations to ensure accuracy and resolve any inconsistencies.