If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?
Practice Questions
1 question
Q1
If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?
Acute
Obtuse
Right
Equilateral
A triangle with sides 3, 4, and 5 satisfies the Pythagorean theorem, thus it is a right triangle.
Questions & Step-by-step Solutions
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Q
Q: If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?
Solution: A triangle with sides 3, 4, and 5 satisfies the Pythagorean theorem, thus it is a right triangle.
Steps: 5
Step 1: Identify the lengths of the sides of the triangle. Here, the sides are 3, 4, and 5.
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: Determine which side is the longest. In this case, 5 is the longest side.
Step 4: Calculate the squares of the sides: 3^2 = 9, 4^2 = 16, and 5^2 = 25.
Step 5: Check if the Pythagorean theorem holds: 9 + 16 = 25. Since this is true, the triangle is a right triangle.
