In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectiv
Practice Questions
Q1
In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?
Acute
Obtuse
Right
Equilateral
Questions & Step-by-Step Solutions
In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?
Correct Answer: Right triangle
Step 1: Identify the lengths of the sides of triangle ABC. Here, side a = 8, side b = 15, and side c = 17.
Step 2: Use the Pythagorean theorem to check if the triangle is a right triangle. The theorem 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, side c (17) is the longest side.
Step 4: Calculate the squares of the sides: a² = 8² = 64, b² = 15² = 225, and c² = 17² = 289.
Step 5: Add the squares of sides a and b: 64 + 225 = 289.
Step 6: Compare the sum with the square of side c: 289 (which is a² + b²) equals 289 (which is c²).
Step 7: Since the equation holds true (8² + 15² = 17²), conclude that triangle ABC is a right triangle.
