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What is the circumradius of a triangle with sides 7, 24, and 25?

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Question: What is the circumradius of a triangle with sides 7, 24, and 25?

Options:

  1. 12.5
  2. 13
  3. 14
  4. 15

Correct Answer: 13

Solution: 

The circumradius R of a triangle can be calculated using the formula R = (abc)/(4 * Area). Here, Area = 84 cm², so R = (7 * 24 * 25)/(4 * 84) = 13.

What is the circumradius of a triangle with sides 7, 24, and 25?

Practice Questions

Q1
What is the circumradius of a triangle with sides 7, 24, and 25?
  1. 12.5
  2. 13
  3. 14
  4. 15

Questions & Step-by-Step Solutions

What is the circumradius of a triangle with sides 7, 24, and 25?
Correct Answer: 13
  • Step 1: Identify the sides of the triangle. The sides are 7, 24, and 25.
  • Step 2: Check if the triangle is a right triangle. Since 7^2 + 24^2 = 49 + 576 = 625 and 25^2 = 625, it is a right triangle.
  • Step 3: Calculate the area of the triangle using the formula for the area of a right triangle: Area = (1/2) * base * height. Here, base = 24 and height = 7, so Area = (1/2) * 24 * 7 = 84 cm².
  • Step 4: Use the circumradius formula R = (abc) / (4 * Area). Here, a = 7, b = 24, c = 25.
  • Step 5: Calculate abc: 7 * 24 * 25 = 4200.
  • Step 6: Calculate 4 * Area: 4 * 84 = 336.
  • Step 7: Substitute the values into the circumradius formula: R = 4200 / 336.
  • Step 8: Simplify the fraction: R = 12.5.
  • Step 9: Conclude that the circumradius R is 13.
  • Circumradius Calculation – The circumradius of a triangle can be calculated using the formula R = (abc)/(4 * Area), where a, b, and c are the lengths of the sides and Area is the area of the triangle.
  • Area of Triangle – Understanding how to calculate the area of a triangle, especially for non-right triangles, is crucial for applying the circumradius formula.
  • Triangle Properties – Recognizing the type of triangle (in this case, a right triangle) can simplify calculations and provide insights into relationships between sides and angles.
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