Angle ACB = 90 degrees, CD-height drawn from angle ACB, AB = 15 cm, AD = 5.4 cm, find CD

| February 4, 2021 | education

Angle ACB = 90 degrees, CD-height drawn from angle ACB, AB = 15 cm, AD = 5.4 cm, find CD and the perimeter of triangle ABC

1. Calculate the length of the segment BD:

BD = AB – AD = 15 – 5.4 = 9.6 centimeters.

2. Triangle ACB – rectangular, since ∠ACB = 90 °.

2. Calculate the length of the height CD. It is drawn from the top of a right angle. Therefore, according to

properties of a right-angled triangle, is calculated by the formula:

CD = √AD x BD = √5.4 x 9.6 = 7.2 centimeters.

3. We calculate the length of the leg AC (according to the Pythagorean theorem):

AC = √AD² + CD² = √5.4² + 7.2² = √ 29.16 + 51.84 = √81 = 9 centimeters.

4. We calculate the length of the BC leg (according to the Pythagorean theorem):

BC = √AB² – AC² = √15² – 9² = √225 – 81 = √144 = 12 centimeters.

5. We calculate the total length of all sides of a given triangle (perimeter P):

P = 12 + 9 + 15 = 36 centimeters.

Answer: the perimeter of the ACB triangle is 36 centimeters, CD = 7.2 centimeters.



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