The height of a right-angled triangle, drawn to the hypotenuse, divides it into segments 54 cm

The height of a right-angled triangle, drawn to the hypotenuse, divides it into segments 54 cm and 96 cm long. Find the perimeter of the triangle.

1. ВН – the height drawn from the top of the right angle to the base. AH = 54 cm. CH = 96 cm.

2. Length BH is calculated by the formula:

BH = √АH x CH = √54 x 96 = √5184 = 72 cm.

3. Calculate the length of the aircraft side:

ВС = √СН ^ 2 + ВН ^ 2 = √96 ^ 2 + 72 ^ 2 = √9216 + 5184 = √14400 = 120 cm.

4. Calculate the length of the side AB:

AB = √AH ^ 2 + BH ^ 2 = √54 ^ 2 + 72 ^ 2 = √2916 + 5184 = √8100 = 90 cm.

5. АС = АН + СН = 54 + 96 = 150 cm.

6. The perimeter of the triangle ABC = AB + BC + AC = 90 + 120 + 150 = 360 cm.