In triangle ABC a=8 b=9 c=7 then what is radius (a) 2.5 (b)3.5 (c)4.5 (d) 1.5
To find the radius of the triangle, we first need to determine whether the given triangle is a right triangle or not. This is because the radius can be calculated if and only if the triangle is a right triangle.
To check if the triangle is a right triangle, we can apply the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Using the given side lengths, we can apply the Pythagorean theorem as follows:
a^2 + b^2 = c^2
8^2 + 9^2 = 7^2
64 + 81 ≠ 49
Since the equation is not balanced, it implies that the given triangle is not a right triangle. Therefore, we cannot directly calculate the radius.
Hence, the correct answer is (e) The radius cannot be determined.