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21 August, 07:54

Which group of measurements could be the side lengths of a right triangle?

A.

57 in, 86 in, 95 in

B.

47 in, 76 in, 95 in

C.

57 in, 76 in, 95 in

D.

57 in, 76 in, 105 in

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Answers (1)
  1. 21 August, 08:00
    0
    In right angled triangles, according to Pythagoras' theorem, squared of the hypotenuse is equal to the sum of the squares of the other 2 sides of the triangle.

    if the hypotenuse is H and other 2 sides are A and B, then equation is as follows;

    H² = A² + B²

    1. A - 57 in. B - 86 in.

    H² = A² + B²

    H² = 57² + 86²

    H² = 3249 + 7396

    H = √10645

    = 103.17 in.

    third side given is not 103 in therefore this is not a right angled triangle

    2. A - 47 in. B - 76 in.

    H² = A² + B²

    H² = 47² + 76²

    = 2209 + 5776

    H = √7985

    H = 89.3 in.

    third side given is 95 in. therefore this is not a right angled triangle.

    3. A - 57 in. + B - 76 in.

    H² = A² + B²

    H² = 57² + 76²

    = 3249 + 5776

    H = √9025

    H = 95 in.

    third side given is 95 in. therefore this is a right angled triangle.

    4. A - 57 in. B - 76 in.

    As calculated in the third equation with the same side lengths of A and B, hypotenuse should be 95 in. however the third side length given is 105 in. so this is not a right angle triangle
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