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Return to book index Chapter 9 : Right Triangles and Trigonometry
9.2 Problem Solving Help

Lesson 9.2: Help for Exercises 37 and 38 on page 540

For these exercises you may need to use some of the area formulas given in Lesson 6.7 (pages 372 - 374).

For Exercise 37, read the hint and look carefully at the diagram. What is the length of one side of the large square? Use this length to write an expression that represents the area of the large square. What are the five shapes that divide the large square? Write an expression that represents the area of the large square as the sum of the areas of the five shapes. Set the two expressions equal to each other, expand the binomial, and simplify until you can conclude that a2 + b2 = c2. (Remember that (a + b)2 = a2 + 2ab + b2.)

For Exercise 38, read the hint and look carefully at the diagram. One expression will represent the area of the trapezoid (using the formula for area of a trapezoid). The other expression will represent the area of the trapezoid as the sum of the areas of the three shapes that divide the trapezoid. As you work with the equation, remember that your goal is to conclude that a2 + b2 = c2. Use any techniques you learned in algebra to achieve this.