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

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Question: If the sides of triangle XYZ are in the ratio 3:4:5, what type of triangle is it? (2021)

Options:

Correct Answer: Right

Exam Year: 2021

Solution:

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

If the sides of triangle XYZ are in the ratio 3:4:5, what type of triangle is it? (2021)

If the sides of triangle XYZ are in the ratio 3:4:5, what type of triangle is it? (2021)

Step 1: Understand that the sides of triangle XYZ are in the ratio 3:4:5.
Step 2: Recognize that a triangle with sides in the ratio 3:4:5 can be represented as 3x, 4x, and 5x, where x is a positive number.
Step 3: Recall the Pythagorean theorem, which states that in a right 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 the ratio 3:4:5, which is 5x.
Step 5: Apply the Pythagorean theorem: (5x)² = (3x)² + (4x)².
Step 6: Calculate: 25x² = 9x² + 16x².
Step 7: Simplify: 25x² = 25x², which is true.
Step 8: Since the equation holds true, conclude that triangle XYZ is a right triangle.

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