The height of the CD of a right-angled triangle ABC, lowered to the hypotenuse AB, is 4 8/13 dm

| April 8, 2021 | education

The height of the CD of a right-angled triangle ABC, lowered to the hypotenuse AB, is 4 8/13 dm, the projection of the legs on it is 11 1/13 dm. find all sides of this triangle.

Let’s convert the lengths of the segments into irregular fractions. CD = 4 (8/13) = 60/13, AD = 11 (1/13) = 144/13.

The square of the height drawn from the vertex of the right angle is equal to the product of the segments into which it divides the hypotenuse:

(60/13) ^ 2 = (144/13) * BD.

3600/169 = (144/13) * BD.

ВD = 25/13 cm.

Let us determine the length of the hypotenuse AB. AB = AD + BD = 144/13 + 25/13 = 169/13 = 13 cm

From the right-angled triangle ACD, by the Pythagorean theorem, we define the hypotenuse AC.

AC ^ 2 = CD ^ 2 + AD ^ 2 = (60/13) ^ 2 + (144/13) ^ 2 = (3600 + 20736) / 169 = 144.

AC = 12 cm.

From the right-angled triangle ВСD, according to the Pythagorean theorem, we define the hypotenuse ВС.

ВС ^ 2 = ВD ^ 2 + СD ^ 2 = (25/13) ^ 2 + (60/13) ^ 2 = (625 + 3600) / 169 = 25 cm.

BC = 5 cm.

Answer: Length AB = 13 cm, AC = 12 cm, BC = 5 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.