The bisector of a right triangle divides the hypotenuse into segments, the difference of which

The bisector of a right triangle divides the hypotenuse into segments, the difference of which is 4 cm.Find the hypotenuse if the ratios of the legs are 3: 5

Given: Triangle ABC – rectangular; BK – bisector; CB: BA = 3: 5; KA – KC = 4cm. Find CA-?
Solution:
The bisector divides a side into segments that are proportional to the other two sides. Then CK: KA = СВ: BA, СK: KA = 3: 5; let one part of x see then CK = 3x and KA = 5x. Since KA – KC = 4, then 5x – 3x = 4; 2x = 4; x = 2. Therefore, CK = 3 * 2 = 6 cm and CA = 5 * 2 = 10 cm and CA = CK + CA, CA = 6 + 10 = 16 cm.
Answer: 16 centimeters.