Question

Which side lengths form a right triangle? Choose all answers that apply: Choose all answers that apply: (Choice A) A 2 , 3 , 4 2 ​ , 3 ​ , 4 ​ square root of, 2, end square root, comma, square root of, 3, end square root, comma, square root of, 4, end square root (Choice B) B 8 , 3 , 17 8 ​ ,3, 17 ​ square root of, 8, end square root, comma, 3, comma, square root of, 17, end square root (Choice C) C 5 , 6 , 8 5,6,85, comma, 6, comma, 8

Answers

  1. The choice that has side lengths that form a right triangle is only option B
    B. √8, 3, √(17)

    What is a right triangle?

    A right triangle is a triangle that has an interior angle of 90°.
    The properties of the side lengths of a right triangle are;
    The square of the length of the length of the longest side is equal to the sum of the square of the other two sides, which are the legs of the right. triangle.
    The options are;
    A. √2, √3, √4
    B. √8, 3, √17
    C. 5, 6, 8
    Analyzing each of the options, we get;
    Option A
    The longest side, which is the side that has the largest number is √4
    If the triangle forms a right triangle, we should get;
    (√4)² Equals the sum of (√3)² and (√2)²
    (√4)² = 4
    (√3)² = 3
    (√(2)²= 2
    However; 4 ≠ 3 + 2, therefore the triangle in choice A is not a right angle
    Choice B. The length of the longest side is; √(17)
    The square of the longest side is; (√(17))² = 17
    The square of the length of the side with length √8 = (√8)² = 8
    The square of the length of the third side = 3² = 9
    Which indicates;
    The square of the longest side = 17
    The sum of the square of the other two sides = 9 + 8 = 17
    Therefore, the square of the longest side is the same as the square of the other two sides.
    • The triangle in choice B is a right triangle
    Choice C
    The length of the longest side = 8
    The square of the longest side = 8² = 64
    The sum of the square of the other two sides = 5² + 6² = 61
    Therefore;
    The square of the longest side ≠ The sum of the other two sides
    8² ≠ 5² + 6²
    Choice C is not a right triangle
    Learn more about right triangles here:
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