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

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

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

Correct Answer: Right triangle

Step 1: Understand that the sides of triangle ABC are in the ratio 3:4:5.
Step 2: Recognize that the numbers 3, 4, and 5 can represent the lengths of the sides of the triangle.
Step 3: 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 4: Identify the longest side in the ratio 3:4:5, which is 5.
Step 5: Calculate the squares of the sides: 3^2 = 9, 4^2 = 16, and 5^2 = 25.
Step 6: Add the squares of the two shorter sides: 9 + 16 = 25.
Step 7: Compare the sum (25) to the square of the longest side (25).
Step 8: Since 25 equals 25, the triangle satisfies the Pythagorean theorem.
Step 9: Conclude that triangle ABC 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.