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In an isosceles right triangle, if a leg is 4, then the hypotenuse is _______________.

Sagot :

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Answer:

  4√2

Step-by-step explanation:

You want the length of the hypotenuse in an isosceles right triangle with legs of length 4.

Pythagorean theorem

The Pythagorean theorem tells you the relationship between leg lengths (a, b) and the hypotenuse (c).

  c² = a² + b²

For a = b = 4, this tells us ...

  c² = 4² + 4² = 4²(2)

  c = √(4²·2) = 4√2

The length of the hypotenuse is 4√2.

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Additional comment

The ratio of side lengths in an isosceles right triangle is 1 : 1 : √2. This tells you the hypotenuse is √2 times the leg length. It can be helpful to remember this about this "special" right triangle. It can also be referred to as a 45-45-90 right triangle.

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