In triangle RST, if RS = 5 cm, ST = 12 cm, and RT = 13 cm, is triangle RST a rig

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Question: In triangle RST, if RS = 5 cm, ST = 12 cm, and RT = 13 cm, is triangle RST a right triangle?

Options:

Correct Answer: Yes

Solution:

Using the Pythagorean theorem, check if 5^2 + 12^2 = 13^2. 25 + 144 = 169, which is true. Therefore, triangle RST is a right triangle.

In triangle RST, if RS = 5 cm, ST = 12 cm, and RT = 13 cm, is triangle RST a right triangle?

In triangle RST, if RS = 5 cm, ST = 12 cm, and RT = 13 cm, is triangle RST a right triangle?

Step 1: Identify the lengths of the sides of triangle RST. They are RS = 5 cm, ST = 12 cm, and RT = 13 cm.
Step 2: Recall the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
Step 3: Identify the longest side, which is RT = 13 cm. This will be our hypotenuse.
Step 4: Calculate the square of each side: RS^2 = 5^2 = 25, ST^2 = 12^2 = 144, and RT^2 = 13^2 = 169.
Step 5: Add the squares of the two shorter sides: 25 + 144 = 169.
Step 6: Compare the sum from Step 5 with the square of the hypotenuse from Step 4: 169 = 169.
Step 7: Since both sides of the equation are equal, triangle RST is a right triangle.

Pythagorean Theorem – A fundamental principle in geometry that states in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.