If the sides of a triangle are in the ratio 3:4:5, which type of triangle is it?

If the sides of a triangle are in the ratio 3:4:5, which type of triangle is it?

Step 1: Understand that the sides of the triangle are in the ratio 3:4:5.
Step 2: Assign values to the sides based on the ratio. For example, let the sides be 3x, 4x, and 5x, where x is a positive number.
Step 3: Recall the Pythagorean theorem, which states that in a right-angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Step 4: Identify the longest side in our triangle, which is 5x.
Step 5: Apply the Pythagorean theorem: (5x)² = (3x)² + (4x)².
Step 6: Calculate: 25x² = 9x² + 16x².
Step 7: Simplify the equation: 25x² = 25x², which is true.
Step 8: Since the equation holds true, conclude that the triangle is a right-angled triangle.

Triangle Ratios – Understanding the significance of side ratios in determining the type of triangle.
Pythagorean Theorem – Application of the theorem to identify right-angled triangles based on side lengths.