In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
Practice Questions
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Q1
In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, 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 cm, 15 cm, and 17 cm, what is the type of triangle?
Solution: Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Steps: 7
Step 1: Identify the lengths of the sides of triangle ABC. They are 8 cm, 15 cm, and 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. In this case, the longest side is 17 cm.
Step 4: Calculate the square of each side: 8² = 64, 15² = 225, and 17² = 289.
Step 5: Add the squares of the two shorter sides: 8² + 15² = 64 + 225 = 289.
Step 6: Compare the sum with the square of the longest side: 289 (from the sum) equals 17² (which is also 289).
Step 7: Since the sum of the squares of the two shorter sides equals the square of the longest side, triangle ABC is a right triangle.
