In triangle ABC, if the sides are in the ratio 3:4:5, what is the nature of the triangle?
Practice Questions
1 question
Q1
In triangle ABC, if the sides are in the ratio 3:4:5, what is the nature of the triangle?
Equilateral
Isosceles
Right
Scalene
The sides satisfy the Pythagorean theorem, hence it is a right triangle.
Questions & Step-by-step Solutions
1 item
Q
Q: In triangle ABC, if the sides are in the ratio 3:4:5, what is the nature of the triangle?
Solution: The sides satisfy the Pythagorean theorem, hence it is a right triangle.
Steps: 7
Step 1: Identify the sides of the triangle based on the given ratio 3:4:5. Let's say the sides are 3x, 4x, and 5x, where x is a positive number.
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: In our case, the longest side is 5x. So we need to check if (5x)^2 = (3x)^2 + (4x)^2.
Step 4: Calculate (5x)^2, which is 25x^2.
Step 5: Calculate (3x)^2 + (4x)^2. This is 9x^2 + 16x^2 = 25x^2.
Step 6: Since 25x^2 = 25x^2 is true, the sides satisfy the Pythagorean theorem.
Step 7: Therefore, triangle ABC is a right triangle.
