Mathematics
Grade9
Easy

Question

Use the 45-45-90 theorem to solve for the hypotenuse.

  1. 16
  2. 8
  3. 8√2
  4. √16

hintHint:

We are given a right-angled triangle. It is 45°-45°-90° triangle. We are given the length of the it’s two sides. We are asked to find the length of its hypotenuse using the 45°-45°-90° theorem. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.

The correct answer is: 8


    Let the given triangle be ABC
    ∠ABC = 90°
    AB = 4√2
    BC = 4√2
    It is a 45°-45°-90° triangle. The two angles of the triangle are same. It means the sides opposite to the triangle are equal. When a triangle has two sides equal, it is an isosceles triangle.
    We are asked the length of the hypotenuse AC.
    We have to use the 45°-45°-90° theorem.
    The theorem states that, the length of its hypothesis us √2 times the length of its side.
    AC = √2(length of the it’s side).
    AC = √2 × 4√2
    AC = 8
    Therefore, the length of the hypotenuse is 8.

    For such questions, we should the properties of 45°-45°-90° triangle.

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