EXAMPLE 4 In-Class Example 4 A piece of wood is in the shape of a right triangle. One leg is 7 in. longer than the other leg, and the hypotenuse is 9 in. longer than the shortest side. Find the lengths of the sides of the piece of wood. Answer: 8 in., 15 in., 17 in. A community garden sits on a corner lot and is in the shape of a right triangle. One side is 10 ft longer than the shortest side, while the longest side is 20 ft longer than the shortest side. Find the lengths of the sides of the garden. Solution Step 1: Read the problem carefully, and identify what we are being asked to fi nd. Draw a picture. We must fi nd the lengths of the sides of the garden. Step 2: Choose a variable to represent an unknown, and defi ne the other unknowns in terms of this variable. Draw and label the picture. x 10 x length of the shortest side (a leg) x x 10 length of the second side (a leg) x 20 x 20 length of the third side (hypotenuse) Step 3: Translate the information that appears in English into an algebraic equation. We will use the Pythagorean theorem. a2 b2 c2 Pythagorean theorem x2 (x 10)2 (x 20)2 Substitute. Step 4: Solve the equation. x2 (x 10)2 (x 20)2 x2 x2 20x 100 x2 40x 400 Multiply using FOIL. 2x2 20x 100 x2 40x 400 x2 20x 300 0 Write in standard form. (x 30)(x 10) 0 Factor. b R x 30 0 or x 10 0 Set each factor equal to 0. x 30 or x 10 Solve. Step 5: Check the answer, and interpret the solution as it relates to the problem. The length of the shortest side, x, cannot be a negative number, so x cannot equal 10. Therefore, the length of the shortest side must be 30 ft. The length of the second side x 10, so 30 10 40 ft. The length of the longest side x 20, so 30 20 50 ft. Do these lengths satisfy the Pythagorean theorem? Yes. a2 b2 c2 (30)2 (40)2 (50)2 900 1600 2500 ✓ Therefore, the lengths of the sides are 30 ft, 40 ft, and 50 ft. How did Example 4 compare with Example 3? What was different? YOU TRY 4 A wire is attached to the top of a pole. The pole is 2 ft shorter than the wire, and the distance from the wire on the ground to the bottom of the pole is 9 ft less than the length of the wire. Find the length of the wire and the height of the pole. Wire Pole 436 CHAPTER 7 Factoring Polynomials www.mhhe.com/messersmith
messersmith_power_introductory_algebra_1e_ch4_7_10
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