In triangle ABC, if the lengths of the sides are in the ratio 3:4:5, what type o

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Question: In triangle ABC, if the lengths of the sides are in the ratio 3:4:5, what type of triangle is it?

Options:

Correct Answer: Right

Solution:

Since the sides are in the ratio of a Pythagorean triplet (3, 4, 5), triangle ABC is a right triangle.

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

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

Step 1: Identify the sides of triangle ABC based on the given ratio 3:4:5. This means if one side is 3x, the second side is 4x, and the third side is 5x for some positive number x.
Step 2: Recognize that the sides 3, 4, and 5 form a Pythagorean triplet. This means they satisfy 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: Check the Pythagorean theorem: 5^2 = 3^2 + 4^2. Calculate: 25 = 9 + 16, which simplifies to 25 = 25.
Step 4: Since the equation holds true, conclude that triangle ABC is a right triangle.

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