The height of a right-angled triangle drawn to the hypotenuse divides it into segments

The height of a right-angled triangle drawn to the hypotenuse divides it into segments, one of which is 27 cm, find the perimeter of the triangle if the height is 36 cm.

1. Calculate the length of the CH segment:

BH = √CH x AH.

BH ^ 2 = CH x AH.

CH = 36 ^ 2: 27 = 1296: 27 = 48 cm.

2. Triangles ABH and СBH are rectangular, since BH is the height.

3. Calculate the length of the side AB:

AB = √BH ^ 2 + AH ^ 2 = √36 ^ 2 + 27 ^ 2 = √2025 = 45 cm.

4. Calculate the length of the aircraft side:

ВС = √СН ^ 2 + ВН ^ 2 = √48 ^ 2 + 36 ^ 2 = √3600 = 60 cm.

5. We calculate the length of the side of the speaker:

AC = AH + CH = 27 + 48 = 75 cm.

6. The total length of the sides of the triangle ABC (perimeter) = AC + AB + BC = 75 + 45 + 60 = 180 cm.