What is the circumradius of a triangle with sides 3 cm, 4 cm, and 5 cm? (2021)

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Question: What is the circumradius of a triangle with sides 3 cm, 4 cm, and 5 cm? (2021)

Options:

Correct Answer: 5 cm

Exam Year: 2021

Solution:

For a right triangle, the circumradius R = hypotenuse/2 = 5/2 = 2.5 cm.

What is the circumradius of a triangle with sides 3 cm, 4 cm, and 5 cm? (2021)

What is the circumradius of a triangle with sides 3 cm, 4 cm, and 5 cm? (2021)

Step 1: Identify the sides of the triangle. The sides are 3 cm, 4 cm, and 5 cm.
Step 2: Determine if the triangle is a right triangle. A triangle is a right triangle if the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides.
Step 3: Calculate the squares of the sides: 3^2 = 9, 4^2 = 16, and 5^2 = 25.
Step 4: Check if 5^2 equals 3^2 + 4^2. That is, check if 25 equals 9 + 16.
Step 5: Since 25 equals 25, the triangle is a right triangle.
Step 6: Use the formula for the circumradius R of a right triangle, which is R = hypotenuse / 2.
Step 7: Substitute the hypotenuse (5 cm) into the formula: R = 5 / 2.
Step 8: Calculate R: 5 / 2 = 2.5 cm.

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