The height of the rectangle drawn from the top of the right angle divides the hypotenuse into segments

| March 9, 2021 | education

The height of the rectangle drawn from the top of the right angle divides the hypotenuse into segments, one of which is 25 cm and the other 9 cm, find the sides of this triangle and the area.

By the property of the height of a right-angled triangle. Omitted from the top of an acute angle, the length of the height is equal to the square root of the product of the segments into which the height divides the base.

BH = AD * CD = 25 * 9 = 225 = 15 cm.

From the right-angled triangle ABD, by the Pythagorean theorem, we determine the length AB.

AB ^ 2 = AD ^ 2 + BD ^ 2 = 25 ^ 2 + 15 ^ 2 = 625 + 225 = 850.

AB = √850 = 5 * √34 cm.

From the right-angled triangle ВСD we define the side ВС.

ВС ^ 2 = ВD ^ 2 + СD ^ 2 = 15 ^ 2 + 9 ^ 2 = 225 + 81 =

BC = 3 * √34 cm.

Determine the area of ​​the triangle ABC.

Savs = АС * ВD / 2 = 34 * 15/2 = 255 cm2.

Answer: The lengths of the sides of the triangle are equal: 34 cm, 5 * √34 cm, 3 * √34 cm, the area is 255 cm2.



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