The hypotenuse AB of right triangle ABC is 2 roots of 22, and leg BC is 6 cm Find the length of the median BK.
| May 30, 2021 | education
Let us determine the length of the leg AC by the Pythagorean theorem.
AC ^ 2 = AB ^ 2 – BC ^ 2 = (2 * √22) ^ 2 – 6 ^ 2 = 88 – 36 = 52.
AC = √52 cm.
Since BK is the median, then AK = CK = √52 / 2 cm.
From the right-angled triangle BK, according to the Pythagorean theorem, we determine the length of the hypotenuse BK.
BK ^ 2 = BC ^ 2 + CK ^ 2 = 6 ^ 2 + (√52 / 2) ^ 2 = 36 + 13 = 49.
BK = 7 cm.
Answer: The length of the median BK is 7 cm.
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