What is the circumradius of a triangle with sides 7, 24, and 25?
Practice Questions
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Q1
What is the circumradius of a triangle with sides 7, 24, and 25?
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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.
Questions & Step-by-step Solutions
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Q
Q: What is the circumradius of a triangle with sides 7, 24, and 25?
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.
Steps: 9
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.
