The height CD of a right-angled triangle C divides the hypotenuse into segments AD = 1cm

| March 22, 2021 | education

The height CD of a right-angled triangle C divides the hypotenuse into segments AD = 1cm and DB = 8cm. Find AB, CD, AC, CB

The length of the segment AB = (AD + BD) = (1 + 8) = 9 cm.

Since triangle ABC is rectangular, and its height CD is drawn from the vertex of a right angle, then the square of its length is equal to the product of the segments into which CD divides AB.

CD ^ 2 = AD * BD = 1 * 8 = 8.

СD = 2 * √2 cm.

From the right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the hypotenuse AC.

AC ^ 2 = AD ^ 2 + CD ^ 2 = 1 + 8 = 9.

AC = 3 cm.

In a right-angled triangle BCD, according to the Pythagorean theorem, BC ^ 2 = CD ^ 2 + BD ^ 2 = 8 + 64 = 72.

BC = 6 * √2 cm.

Answer: The lengths of the sides of the triangle are 9 cm, 3 cm, 6 * √2 cm, the height of the triangle is 2 * √2 cm.



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