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SOLUTION

17 2. =. h 2. + 15 2. h 2. + 225. 289. =. h 2. 64. =. h. 8. =. Finding Perimeter and Area. EXAMPLE 2. Find the perimeter and area of the triangle. SOLUTION. STEP 1. Find the height of the triangle. Pythagorean Theorem. Evaluate powers. Subtract 225 from each side.

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SOLUTION

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  1. 172 = h2 + 152 h2 + 225 289 = h2 64 = h 8 = Finding Perimeter and Area EXAMPLE 2 Find the perimeter and area of the triangle. SOLUTION STEP 1 Find the height of the triangle. Pythagorean Theorem Evaluate powers. Subtract 225 from each side. Take positive square root of each side.

  2. 40 = 8 + 15 + 17 = = 60 = (15) (8) 1 2 ANSWER 2 The perimeter is 40cm and the area is 60cm . Finding Perimeter and Area EXAMPLE 2 STEP 2 Use the height to find the perimeter and area. Perimeter Area

  3. Use the converse of the Pythagorean Theorem to determine whether the side lengths of the triangle form a Pythagorean triple. 2 2 a + b = 2 2 c 37 2 2 ? = 12 + 35 ? 1369 144 +1225 = 1369 1369 = Identifying a Pythagorean Triple EXAMPLE 3 Definition of Pythagorean triple Substitute 12 for a, 35 for b, and 37 for c. Evaluate powers. Add.

  4. ANSWER = Because and the side lengths are integers, the side lengths form a Pythagorean triple. 2 37 2 2 12 + 35 Identifying a Pythagorean Triple EXAMPLE 3

  5. ANSWER The Perimeteris 168ft and the area is 840ft 2? for Examples 2 and 3 GUIDED PRACTICE 3. Find the perimeter and area of a right triangle that has a hypotenuse of length 74 feetand a leg of length 70 feet.

  6. 4. Determine whether the side lengths of the triangle form a Pythagorean triple. for Examples 2 and 3 GUIDED PRACTICE ANSWER No

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