In triangle XYZ, if side XY = 8 cm, side YZ = 6 cm, and side XZ = 10 cm, which o

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Question: In triangle XYZ, if side XY = 8 cm, side YZ = 6 cm, and side XZ = 10 cm, which of the following is true?

Options:

Correct Answer: It is a right triangle.

Solution:

Using the Pythagorean theorem, since 10^2 = 8^2 + 6^2 (100 = 64 + 36), triangle XYZ is a right triangle.

In triangle XYZ, if side XY = 8 cm, side YZ = 6 cm, and side XZ = 10 cm, which of the following is true?

In triangle XYZ, if side XY = 8 cm, side YZ = 6 cm, and side XZ = 10 cm, which of the following is true?

Step 1: Identify the lengths of the sides of triangle XYZ. They are XY = 8 cm, YZ = 6 cm, and XZ = 10 cm.
Step 2: Recognize that the longest side (XZ = 10 cm) could be the hypotenuse of a right triangle.
Step 3: Use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is c^2 = a^2 + b^2.
Step 4: Assign the sides: let a = XY = 8 cm, b = YZ = 6 cm, and c = XZ = 10 cm.
Step 5: Calculate a^2: 8^2 = 64.
Step 6: Calculate b^2: 6^2 = 36.
Step 7: Calculate c^2: 10^2 = 100.
Step 8: Add a^2 and b^2: 64 + 36 = 100.
Step 9: Compare c^2 with a^2 + b^2: Since 100 = 100, the equation holds true.
Step 10: Conclude that triangle XYZ is a right triangle because it satisfies the Pythagorean theorem.

Pythagorean Theorem – A mathematical principle used to determine if a triangle is a right triangle by checking if the square of the longest side equals the sum of the squares of the other two sides.
Triangle Inequality Theorem – A principle stating that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.