Given 2 mutually perpendicular planes alpha and beta. ОА and ОВ are perpendicular to the line

Given 2 mutually perpendicular planes alpha and beta. ОА and ОВ are perpendicular to the line of intersection of the planes. AB = 80cm. OA: OB = 6: 8. Find OA, OВ?

Since the planes α and β are perpendicular, and the segments OA and OB are perpendicular to the line of intersection, the angle AOB is straight, and the triangle AOB is rectangular.
Let the side length OA = 6 * X cm, then OB = 8 * X cm.
By the Pythagorean theorem, AB2 = OA2 + OB2.
6400 = 36 * X2 + 64 * X2.
100 * X2 = 6400.
X2 = 64.
X = 8.
Then ОА = 6 * 8 = 48 cm, ОВ = 8 * 8 = 64 cm.
Answer: The length of the segment OA is 48 cm, OВ is 64 cm.