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Question
What is the length of the hypotenuse in the triangle shown below?

Question\newlineWhat is the length of the hypotenuse in the triangle shown below?

Full solution

Q. Question\newlineWhat is the length of the hypotenuse in the triangle shown below?
  1. Identify triangle and sides: Identify the right triangle and the sides given. Assume the sides are 3cm3\,\text{cm} and 4cm4\,\text{cm} as the legs of the triangle.
  2. Apply Pythagorean theorem: Apply the Pythagorean theorem, which states a2+b2=c2 a^2 + b^2 = c^2 , where c c is the hypotenuse. Here, a=3 a = 3 cm and b=4 b = 4 cm.
  3. Calculate squares: Calculate the square of each side: 32=9 3^2 = 9 and 42=16 4^2 = 16 .
  4. Add squares: Add the squares of the legs: 9+16=25 9 + 16 = 25 .
  5. Find hypotenuse length: Find the square root of 2525 to get the length of the hypotenuse: 25=5 \sqrt{25} = 5 cm.

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