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Unformatted text preview: e is 9 and whose altitude is 4. Find the perimeter of the square. (A) 36 (B) 26 (C) 13 (D) 24 (E) none of these 2. 5. 3. www.petersons.com Geometry 205 3. RIGHT TRIANGLES
A. Pythagorean theorem
(leg)2 + (leg)2 = (hypotenuse)2 ( 5 )2 + ( 2 )2 = x 2
25 + 4 = x 2 29 = x 2 x = 29 B. Pythagorean triples
These are sets of numbers that satisfy the Pythagorean Theorem. When a given set of numbers such as 3, 4, 5 forms a Pythagorean triple (32 + 42 = 52), any multiples of this set such as 6, 8, 10 or 30, 40, 50 also form a Pythagorean triple. Memorizing the sets of Pythagorean triples that follow will save you valuable time in solving problems, for, if you recognize given numbers as multiples of Pythagorean triples, you do not have to do any arithmetic at all. The most common Pythagorean triples that should be memorized are 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 Squaring 34 and 16 to apply the Pythagorean theorem would take too much time. Instead, recognize the hypotenuse as 2(17). Suspect an 8, 15, 17 triangle. Since the given leg is 2(8), the missing leg will be 2(15) or 30, without any computation at all. www.petersons.com 206 Chapter 13 C. 30°–60°–90° triangle
a) The leg opposite the 30° angle is onehalf the hypotenuse. b) The leg opposite the 60° angle is onehalf the hypotenuse · 3 . c) An altitude in an equilateral triangle forms a 30°–60°–90° triangle and is therefore equal to onehalf the side · 3 . D. 45°–45°–90° triangle (isosceles right triangle)
a) b) c) Each leg is onehalf the hypotenuse times Hypotenuse is leg times
2. 2. 2. The diagonal of a square forms a 45°–45°–90° triangle and is therefore equal to a side times www.petersons.com Geometry 207 Exercise 3
Work out each problem. Circle the letter that appears before your answer. 1. A farmer uses 140 feet of fencing to enclose a rectangular field. If the ratio of length to width is 3 : 4, find the diagonal, in feet, of the field. (A) 50 (B) 100 (C) 20 (D) 10 (E) cannot be determined Find the altitude of an equilateral triangle whose side is 20. (A)...
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 Spring '10
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