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# Right Triangles Geometric Mean

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 Sub Topics When one side of triangle is makes an angle of 90 degrees, then given triangle is called as a Right Triangle means each right triangle has 90 degree angle. As we all know that geometric Mean of 2 Numbers are √ (a * b), where ‘a’ and ‘b’ are two numbers. Now we will discuss how to find out geometric mean in right Triangles. For calculating Altitude of right triangle, we use geometric mean between 2 hypotenuses, so geometric mean in right triangle is, Altitude of right triangle = √ (length of hypotenuse-1 * length of hypotenuse-2), Suppose we have two hypotenuse length of right triangle is 4 inch and 6 inch, then altitude of right triangle is – Altitude of right triangle = √ (length of hypotenuse-1 * length of hypotenuse-2), = √ (6 * 4), = √ 24, = 4.94. So, altitude of right is 4.94 inch, where other 2 hypotenuse length is 6 inch and 4 inch. Altitude of right triangle divides triangle into two parts, where altitude is part of both sides like we have a right triangle ABC, where ‘BD’ is an altitude of given right triangle, then by altitude geometric mean right triangles theorem– AD / BD = BD / CD, = > (BD)2 = AD * CD, So, altitude BD is behaving like geometric mean of given hypotenuse length of right triangle, which is AD and CD means AD and CD both are hypotenuse length of right triangle. Suppose we have a right triangle PQR, where PS is an altitude and hypotenuse length of RS = 8 inch and QS = 6 inch, then, Here we apply geometric mean theorem for evaluation of altitude PS– PS = √ (length of RS * length of QS), = √ (8 * 6), = √ 48, = 6.91. So, altitude of right triangle PQR is 6.91 inch.