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determine if a triangle with sides of lengths 4 cm, 9 cm, and 10 cm is a right triangle and explain how you know.

User Grantespo
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Final answer:

Applying the Pythagorean theorem, the triangle with sides of lengths 4 cm, 9 cm, and 10 cm is not a right triangle because 4² + 9² (which equals 97) does not equal 10² (which is 100).

Step-by-step explanation:

To determine if a triangle with sides of lengths 4 cm, 9 cm, and 10 cm is a right triangle, we use the Pythagorean theorem. According to this theorem, the square of the hypotenuse's length—the side that faces the right angle—in a right triangle equals the sum of the squares of the lengths of the other two sides. The formula is represented as a² + b² = c², where c is the hypotenuse and a and b are the other two sides of the triangle.

Let's apply this formula to our triangle with sides 4 cm, 9 cm, and 10 cm:

  • For sides 4 cm (a) and 9 cm (b), the sum of their squares is 4² + 9² = 16 + 81 = 97.
  • The square of the longest side, 10 cm (c), is 10² = 100.

Since 97 does not equal 100, the triangle with sides of lengths 4 cm, 9 cm, and 10 cm is not a right triangle.

User Nuno Furtado
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