In triangle STU, if ST = 7 cm, TU = 24 cm, and SU = 25 cm, is triangle STU a rig

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Question: In triangle STU, if ST = 7 cm, TU = 24 cm, and SU = 25 cm, is triangle STU a right triangle?

Options:

Correct Answer: Yes

Solution:

Using the Pythagorean theorem, 7^2 + 24^2 = 49 + 576 = 625, which equals 25^2. Therefore, triangle STU is a right triangle.

In triangle STU, if ST = 7 cm, TU = 24 cm, and SU = 25 cm, is triangle STU a right triangle?

In triangle STU, if ST = 7 cm, TU = 24 cm, and SU = 25 cm, is triangle STU a right triangle?

Step 1: Identify the lengths of the sides of triangle STU. They are ST = 7 cm, TU = 24 cm, and SU = 25 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: Determine which side is the hypotenuse. In this case, SU = 25 cm is the longest side, so it is the hypotenuse.
Step 4: Calculate the square of the lengths of the two shorter sides: ST^2 = 7^2 = 49 and TU^2 = 24^2 = 576.
Step 5: Add these two results together: 49 + 576 = 625.
Step 6: Now calculate the square of the hypotenuse: SU^2 = 25^2 = 625.
Step 7: Compare the two results: 625 (from the sum of the squares of the shorter sides) equals 625 (from the square of the hypotenuse).
Step 8: Since both results are equal, triangle STU is a right triangle.

Pythagorean Theorem – A mathematical principle 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.