In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, what type of triangle
Practice Questions
Q1
In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, what type of triangle is it?
Acute
Obtuse
Right
Equilateral
Questions & Step-by-Step Solutions
In triangle XYZ, if XY = 5 cm, YZ = 12 cm, and XZ = 13 cm, what type of triangle is it?
Step 1: Identify the lengths of the sides of triangle XYZ. They are XY = 5 cm, YZ = 12 cm, and XZ = 13 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Step 3: Identify the longest side, which is XZ = 13 cm. This will be our hypotenuse.
Step 4: Calculate the square of each side: XY^2 = 5^2 = 25, YZ^2 = 12^2 = 144, and XZ^2 = 13^2 = 169.
Step 5: Add the squares of the two shorter sides: 5^2 + 12^2 = 25 + 144 = 169.
Step 6: Compare this sum to the square of the hypotenuse: 169 = 13^2.
Step 7: Since the equation holds true (25 + 144 = 169), triangle XYZ is a right triangle.
