Question: If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, is it a right triangle?
Options:
Yes
No
Not enough information
Only if angles are known
Correct Answer: Yes
Solution:
Yes, because 3² + 4² = 5² (9 + 16 = 25).
If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, is it a right triangle?
Practice Questions
Q1
If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, is it a right triangle?
Yes
No
Not enough information
Only if angles are known
Questions & Step-by-Step Solutions
If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, is it a right triangle?
Step 1: Identify the lengths of the sides of the triangle. They are 3 cm, 4 cm, and 5 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 5 cm.
Step 4: Calculate the square of the lengths of the sides: 3² = 9, 4² = 16, and 5² = 25.
Step 5: Add the squares of the two shorter sides: 3² + 4² = 9 + 16 = 25.
Step 6: Compare the sum from Step 5 with the square of the longest side from Step 4: 25 = 25.
Step 7: Since both sides are equal, conclude that the triangle is a right triangle.
Pythagorean Theorem – The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
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