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

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Question: If the sides of a triangle are in the ratio 3:4:5, what type of triangle is it? (2022)

Options:

Correct Answer: Right-angled

Exam Year: 2022

Solution:

A triangle with sides in the ratio 3:4:5 satisfies the Pythagorean theorem, hence it is a right-angled triangle.

If the sides of a triangle are in the ratio 3:4:5, what type of triangle is it? (2022)

If the sides of a triangle are in the ratio 3:4:5, what type of triangle is it? (2022)

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: 25x^2 = 9x^2 + 16x^2.
Step 7: Simplify the equation: 25x^2 = 25x^2, 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 – Applying the theorem to identify right-angled triangles based on side lengths.