What is the circumradius of a triangle with sides 3 cm, 4 cm, and 5 cm? (2021)
Practice Questions
Q1
What is the circumradius of a triangle with sides 3 cm, 4 cm, and 5 cm? (2021)
2 cm
3 cm
4 cm
5 cm
Questions & Step-by-Step Solutions
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.
