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20 October, 16:23

Which set of numbers can represent the side lengths, in centimeters, of a right triangle?

0 8, 12, 15

O 10, 24, 26

O 12, 20, 25

15, 18, 20

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  1. 20 October, 16:30
    0
    The set {10, 24, 26} formed a right triangle

    Step-by-step explanation:

    * Lets explain how to check the sides lengths which formed a

    right triangle

    - In triangle ABC

    # If AC is the longest side in length

    # If (AC) ² = (AB) ² + (BC) ²

    ∴ AB, BC, AC formed a right angle triangle

    ∴ m∠B = 90° (The angle opposite to the longest side)

    ∴ AC is the hypotenuse

    * Now lets solve the problem

    - In set 8, 12, 15

    ∵ The longest side is 15 cm

    ∴ (15) ² = 225

    ∵ (8) ² + (12) ² = 64 + 144 = 208

    ∵ (15) ² ≠ (8) ² + (12) ²

    ∴ The set not formed a right triangle

    - In set 10, 24, 26

    ∵ The longest side is 26 cm

    ∴ (26) ² = 676

    ∵ (10) ² + (24) ² = 100 + 576 = 676

    ∵ (26) ² = (10) ² + (24) ²

    ∴ The set formed a right triangle

    - In set 12, 20, 25

    ∵ The longest side is 25 cm

    ∴ (25) ² = 625

    ∵ (12) ² + (20) ² = 144 + 400 = 544

    ∵ (25) ² ≠ (12) ² + (20) ²

    ∴ The set not formed a right triangle

    - In set 15, 18, 20

    ∵ The longest side is 20 cm

    ∴ (20) ² = 400

    ∵ (15) ² + (18) ² = 225 + 324 = 549

    ∵ (20) ² ≠ (15) ² + (18) ²

    ∴ The set not formed a right triangle

    * The set {10, 24, 26} formed a right triangle
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