The height of a right-angled triangle, drawn from the vertex of the right angle, divides the hypotenuse

The height of a right-angled triangle, drawn from the vertex 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.

Given:
Right-angled triangle ABC
angle C = 90 degrees
CH – height
AH = 25 cm
HB = 9 cm
Find: CA, СB, AB and S -?
Decision:
1) We know that the height that is dropped from the top of the right angle is equal to:
CH = √ (AH * HB),
CH = √ (25 * 9);
CH = √225;
CH = 15 cm;
2) S = 1/2 * CH * AB,
AB = AH + HB = 25 + 9 = 34 (cm);
S = 1/2 * 15 * 34 = 255 cm ^ 2
3) Triangle СBН – rectangular. By the Pythagorean theorem:
CB ^ 2 = CH ^ 2 + HB ^ 2;
CB ^ 2 = 15 ^ 2 + 9 ^ 2;
CB ^ 2 = 225 + 81;
CB ^ 2 = 306;
CB = 3√34 cm;
4) The CBA triangle is rectangular. By the Pythagorean theorem:
CA ^ 2 = CH ^ 2 + AH ^ 2;
CA ^ 2 = 15 ^ 2 + 25 ^ 2;
CA ^ 2 = 225 + 625;
CA ^ 2 = 850;
CA = 5√34 cm.
Answer: 5√34 cm; 3√34 cm; 34 cm; 255 cm ^ 2.