Answer:
[tex]SP = \frac{TO^{2} }{RQ}[/tex] (TO being the center line)
Step-by-step explanation:
I helped my nephew with a similar problem yesterday. From this image you can draw a few conclusions. Observe the middle line with the width 45. Let's call this line TO where the point T is on the left side and O is on the right side. Since the distance from R to T is equal to the distance from S to T, and similarly the distance from P to O is equal to the distance from Q to O, we can know that RQ relates to TO as TO relates to SP. Written in mathematical form this means,
[tex]\frac{SP}{TO} = \frac{TO}{RQ}[/tex]
Since we know the values of RQ and TO we can easily solve for SP.
[tex]\frac{SP}{TO} = \frac{TO}{RQ} \implies\\\frac{SP}{45} = \frac{45}{64} \implies\\\frac{SP*45}{45} = \frac{45*45}{64} \implies\\SP = \frac{45^{2}}{64} = \frac{2025}{64}[/tex]or [tex]SP = \frac{TO^{2} }{RQ}[/tex]
If you have any questions about this explanation, just reply with a comment. :)
