In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, is triangle ABC a right triangle?
Practice Questions
1 question
Q1
In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, is triangle ABC a right triangle?
Yes
No
Cannot be determined
Only if angle A is 90°
Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2, so triangle ABC is a right triangle.
Questions & Step-by-step Solutions
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Q
Q: In triangle ABC, if AB = 7 cm, AC = 24 cm, and BC = 25 cm, is triangle ABC a right triangle?
Solution: Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625 = 25^2, so triangle ABC is a right triangle.
Steps: 8
Step 1: Identify the lengths of the sides of triangle ABC. We have AB = 7 cm, AC = 24 cm, and BC = 25 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Step 3: Identify the longest side, which is BC = 25 cm. This will be our hypotenuse.
Step 4: Calculate the square of the lengths of the two shorter sides: AB^2 = 7^2 = 49 and AC^2 = 24^2 = 576.
Step 5: Add these two results together: 49 + 576 = 625.
Step 6: Now calculate the square of the hypotenuse: BC^2 = 25^2 = 625.
Step 7: Compare the two results: 625 (from the sum of the squares of the shorter sides) is equal to 625 (the square of the hypotenuse).
Step 8: Since the two results are equal, triangle ABC is a right triangle.
