In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type
Practice Questions
Q1
In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?
Acute
Obtuse
Right
Equilateral
Questions & Step-by-Step Solutions
In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?
Correct Answer: Right Triangle
Step 1: Identify the lengths of the sides of triangle ABC. They are 8, 15, and 17.
Step 2: Use the Pythagorean theorem to check if it is a right triangle. The theorem states that in a right triangle, the square 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, the longest side is 17.
Step 4: Calculate the square of the longest side: 17² = 289.
Step 5: Calculate the squares of the other two sides: 8² = 64 and 15² = 225.
Step 6: Add the squares of the two shorter sides: 64 + 225 = 289.
Step 7: Compare the results: Since 8² + 15² = 17² (289 = 289), triangle ABC satisfies the Pythagorean theorem.
Step 8: Conclude that triangle ABC is a right triangle.
