The length of OP in triangle MNO, with NP as the altitude, is 5.4 units.
In the given right-angled triangle MNO, NP is the altitude drawn to the hypotenuse. According to the altitude-on-hypotenuse theorem, the length of the altitude NP can be expressed as the geometric mean of the two segments it divides the hypotenuse into, which are MP and OP. The formula is:
NP^2 = MP * OP
Given that NP = 9 and MP = 15, we can substitute these values into the formula:
9^2 = 15 * OP
Simplifying:
81 = 15 * OP
Now, solve for OP:
OP = 81/15
OP = 5.4
Therefore, the length of OP is 5.4 units.
In summary, applying the altitude-on-hypotenuse theorem allows us to determine that the length of OP is 5.4 units.