Answer
See the detailed answer below.
Work Step by Step
We need to make a non-inverting telescope with a magnification of $100\times$ by using three lenses of 150 cm-focal lengths, 1.5 cm, and 10 cm.
We know that the magnification of a telescope is given by
$$M=-\dfrac{f_o}{f_e}$$
where $f_o$ is the focal length of the objective lens while $f_e$ is the focal length of the eyepiece lens.
Thus, from the three given lenses, we can use only two lenses to get this magnification and it is obvious that these lenses are the 150 cm as an objective lens and the 1.5 cm lens as an eyepiece lens.
Thus,
$$M=-\dfrac{150}{1.5}=100\times$$
Now we need to find where we can put the third lens and the distances between the lenses.
We know that the objective lens creates an image at its focal point and this image will be the object of the third lens (which has a focal length of 10 cm). This third lens must be placed away from the image of the objective lens by a distance of twice its focal length.
This means that the first image will be 20 cm away from the third lens and 150 cm away from the objective lens.
Also, this third lens must be 21.5 cm away from the eyepiece lens.
See the figure below.
Now the length of the telescope is given by
$$L=150+40+1.5=191.5\;\rm cm\approx 2\;m$$
So, the length of this telescope is about 2 meters.
