In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?
Practice Questions
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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
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Questions & Step-by-step Solutions
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Q
Q: In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?
Solution: Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Steps: 8
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.
