In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, is it a right triangl
Practice Questions
Q1
In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, is it a right triangle?
Yes
No
Cannot be determined
Only if XY is the hypotenuse
Questions & Step-by-Step Solutions
In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, is it a right triangle?
Step 1: Identify the lengths of the sides of triangle XYZ. They are XY = 8 cm, YZ = 15 cm, and XZ = 17 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 3: Identify the longest side. Here, XZ = 17 cm is the longest side.
Step 4: Calculate the square of each side: XY^2 = 8^2 = 64, YZ^2 = 15^2 = 225, and XZ^2 = 17^2 = 289.
Step 5: Add the squares of the two shorter sides: 64 + 225 = 289.
Step 6: Compare the sum from Step 5 with the square of the longest side from Step 4: 289 = 289.
Step 7: Since the two values are equal, conclude that triangle XYZ is a right triangle.
