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