In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?
Practice Questions
1 question
Q1
In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?
Acute
Obtuse
Right
Equilateral
Since 7² + 24² = 49 + 576 = 625 = 25², triangle ABC is a right triangle.
Questions & Step-by-step Solutions
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Q
Q: In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what type of triangle is it?
Solution: Since 7² + 24² = 49 + 576 = 625 = 25², triangle ABC is a right triangle.
Steps: 7
Step 1: Identify the lengths of the sides of triangle ABC. Here, side a = 7, side b = 24, and side c = 25.
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, side c (25) is the longest side.
Step 4: Calculate the square of each side: a² = 7² = 49, b² = 24² = 576, and c² = 25² = 625.
Step 5: Add the squares of sides a and b: 49 + 576 = 625.
Step 6: Compare the sum from Step 5 with the square of side c: 625 = 625.
Step 7: Since the equation from Step 6 is true, triangle ABC is a right triangle.
