Question

what is the circum radius of triangle whose side are 7,24 and 25 units respectively

Answer 1

this is a right angled triangle. so circumradius is half of hypotenuse. circumradius is 25/2 i.e 12.5 units
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Answer 2

Concept-

The question requires the understanding of some properties of a triangle.

Given-

Sides of a triangle are given as 7, 24 and 25 cm respectively.

Find-

We need to seek out the circumradius of a triangle whose sides are given as 7, 25 and 25.

Solution-

a = 7 cm , b = 24 cm , c = 25 cm

Then, length of the longest side is c = 25 cm

∴ c = 25² = 625

and a² + b² = (7)² + (24)²

⇒ a² + b² = 49 + 576

⇒ a² + b² = 625

∴ c² = a² + b²

i.e. , (25)² = (7)² + (24)²

If  sides of a triangle are given in this form , it clearly indicates that the given triangle is a right angled triangle.

Now, in the right angled triangle, the median to the hypotenuse is half the hypotenuse and  it is also the circumradius of a triangle.

If the hypotenuse is 25 cm, the circumradius must be 12.5 cm.

Hence, the circumradius of a triangle is 12.5 cm

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