In triangle XYZ, if side XY = 8 cm, side YZ = 6 cm, and side XZ = 10 cm, which o
Practice Questions
Q1
In triangle XYZ, if side XY = 8 cm, side YZ = 6 cm, and side XZ = 10 cm, which of the following is true?
It is a right triangle.
It is an obtuse triangle.
It is an acute triangle.
It cannot be classified.
Questions & Step-by-Step Solutions
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.
