1. SOLUTION Finding Perimeter and Area STEP 1 Find the perimeter and area of the triangle. Find the height of the triangle. Pythagorean Theorem Evaluate powers. Subtract 225 from each side. Take positive square root of each side. h 8 = EXAMPLE 2 + 225 = 289h2h2 = 64h2h2 = h2h2 + 15 2 17 2

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

3. EXAMPLE 3 Identifying a Pythagorean Triple Use the converse of the Pythagorean Theorem to determine whether the side lengths of the triangle form a Pythagorean triple. c 2 a + b 22 = = 1369 ? 144 +1225 1369 = Definition of Pythagorean triple Substitute 12 for a, 35 for b, and 37 for c. Evaluate powers. Add. 37 2 = 12 + 35 22 ?

4. EXAMPLE 3 Because and the side lengths are integers, the side lengths form a Pythagorean triple. ANSWER = 37 2 12 + 35 22 Identifying a Pythagorean Triple

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

6. GUIDED PRACTICE for Examples 2 and 3 4. Determine whether the side lengths of the triangle form a Pythagorean triple. ANSWERNo