What is the circumradius of a triangle with sides 5 cm, 12 cm, and 13 cm?

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Question: What is the circumradius of a triangle with sides 5 cm, 12 cm, and 13 cm?

Options:

Correct Answer: 7 cm

Solution:

For a right triangle, circumradius R = hypotenuse / 2 = 13 / 2 = 6.5 cm.

What is the circumradius of a triangle with sides 5 cm, 12 cm, and 13 cm?

What is the circumradius of a triangle with sides 5 cm, 12 cm, and 13 cm?

Step 1: Identify the sides of the triangle. The sides are 5 cm, 12 cm, and 13 cm.
Step 2: Check if the triangle is a right triangle. A right triangle has one angle that is 90 degrees.
Step 3: Use the Pythagorean theorem to check if 5^2 + 12^2 = 13^2. Calculate 5^2 = 25, 12^2 = 144, and 13^2 = 169.
Step 4: Add 5^2 and 12^2: 25 + 144 = 169, which equals 13^2. This confirms it is a right triangle.
Step 5: For a right triangle, the circumradius R can be calculated using the formula R = hypotenuse / 2.
Step 6: The hypotenuse is the longest side, which is 13 cm. So, R = 13 cm / 2.
Step 7: Calculate R: 13 / 2 = 6.5 cm.

Circumradius of a Triangle – The circumradius is the radius of the circumcircle, which is the circle that passes through all the vertices of the triangle. For a right triangle, the circumradius can be calculated as half the length of the hypotenuse.
Right Triangle Properties – In a right triangle, the longest side is the hypotenuse, and the circumradius can be directly derived from it.