Guided Solution To Problem of Week #2

In keeping with our posts on guiding discovery rather than explaining, we present some hints to guide your discovery of the solution to Problem of the Week #2. Do you have other solutions? observations? comments?

1. Touch the shaded triangle. Tell the name of the triangle (“WKX”).
2. The shaded triangle is part of a rectangle. Name the rectangle.
3. What is the area (in square inches) of that rectangle?
4. What is the area of the shaded triangle?
5. What is the area of triangle WXD?
6. What is the area of triangle XYA?
7. What is the area of triangle YZB?
8. What is the area of triangle ZWC?
9. What is the combined area of the four triangles inside the dotted lines (WXD, XYA, YZB, and ZWC)?
10. What is the length of line segment XL?
11. What is the length of line segment AY?
12. What is the length of line segment ZM?
13. What is the length of line segment BY?
14. What is the length of line segment AB?
15. What are the lengths of line segments BC, CD, and DA?
16. Is figure ABCD a square? What is its area?
17. What is the total area inside figure WXYZ?
18. Is WXYZ a square? Here’s how to find out…
19. Angle WDX is a right angle (90°). If you add angles DWX and DXW together, is the sum 90°?
20. Is angle AXY the same as angle DWX?
21. If you add angles DXW and AXY together, is the sum 90°?
22. Can you prove that WXYZ is a square?
23. What is the area of WXYZ?
24. If you know the area of a square, can you determine the length of one of its sides?
25. What is the length of line segment WX?

 

Problem of the Week #2 – Pythagorean Right Triangle

Imagine that you had never heard of the Pythagorean Theorem (a² + b² = c²), and that you did not have a ruler. Using only the drawing below, determine the exact length of line segment WX.
All corners that look square are square. The answer will be posted next week.