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EXAMPLE 3

RQ 2. = RS RT. 16 2. = x ( x + 8). 256. = x 2 + 8 x. 0. = x 2 + 8 x – 256. 8 2 – 4(1) (– 256). –8 +. x. =. 2(1). 17. x. = – 4 + 4. EXAMPLE 3. Find lengths using Theorem 10.16. Use the figure at the right to find RS. SOLUTION. Use Theorem 10.16.

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EXAMPLE 3

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  1. RQ2 = RS RT 162 = x (x + 8) 256 = x2 + 8x 0 = x2 + 8x – 256 82 – 4(1) (– 256) –8 + x = 2(1) 17 x = – 4 + 4 EXAMPLE 3 Find lengths using Theorem 10.16 Use the figure at the right to find RS. SOLUTION Use Theorem 10.16. Substitute. Simplify. Write in standard form. Use quadratic formula. Simplify.

  2. So, x 12.49, andRS 12.49 17 = – 4 + 4 EXAMPLE 3 Find lengths using Theorem 10.16 Use the positive solution, because lengths cannot be negative.

  3. x2 x2 = 4 = 1 (1 + 3) x = 2 for Example 3 GUIDED PRACTICE Find the value of x. 4. SOLUTION Use Theorem 10.16. Simplify. Simplify.

  4. 72 49 = 25 + 5x = 5 (x + 5) = 5x 24 x = 24 5 for Example 3 GUIDED PRACTICE Find the value of x. 5. SOLUTION Use Theorem 10.16. Simplify. Write in standard form. Simplify.

  5. 122 144 = x2 + 10x = x (x + 10) 0 = x2 + 10x – 144 x = 102 – 4(1) (– 144) –10 + x = 8 2(1) for Example 3 GUIDED PRACTICE Find the value of x. 6. SOLUTION Use Theorem 10.16. Simplify. Write in standard form. Use quadratic formula. Simplify.

  6. 152 = x (x + 14) 255 = x2 + 14x 0 = x2 + 14x – 255 x 142 – 4(1) (– 255) –14 + = 2(1) x = – 7 + 274 for Example 3 GUIDED PRACTICE 7. Determine which theorem you would use to find x. Then find the value of x. SOLUTION Theorem 10.16 Use Theorem 10.16. Simplify. Write in standard form. Use quadratic formula. Simplify.

  7. x (18) = (9) (16) 18x = 144 x = 8 for Example 3 GUIDED PRACTICE 8. Determine which theorem you would use to find x. Then find the value of x. SOLUTION Use Theorem 10.14. Substitute. Simplify. Simplify.

  8. 18 (18 + 22) = 29x + x2 720 0 = x2 + 29x – 720 = x (x + 29) x 292 – 4(1) (– 720) –29 + = 2(1) x = 16 for Example 3 GUIDED PRACTICE 8. Determine which theorem you would use to find x. Then find the value of x. SOLUTION Use Theorem 10.15. Substitute. Simplify. Write in standard form. Use quadratic formula. Simplify.

  9. 9. In the diagram for Theorem 10.16, what must be true about ECcompared toEA ? for Example 3 GUIDED PRACTICE SOLUTION EC < EA

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