I want solve next formula for QuantityVariable["t","Time"]

f = FormulaData["PythagoreanTheorem"] /. { 
QuantityVariable["a","Length"]->QuantityVariable["l","Length"], 
QuantityVariable["b","Length"]->QuantityVariable["t","Time"] * QuantityVariable["v","Speed"], 
QuantityVariable["c","Length"]->QuantityVariable["t","Time"] * Quantity[1,"SpeedOfLight"]}

But Solve[f, QuantityVariable["t","Time"]] does nothing.

I want to get next solution

s = {{ QuantityVariable["t","Time"]->Sqrt[QuantityVariable["l","Length"]^2 / (Quantity[1,"SpeedOfLight"]^2 - QuantityVariable["v","Speed"]^2)] }}

To use this like next

s /. {QuantityVariable["l","Length"]->Quantity[10,"Meters"], QuantityVariable["v","Speed"]->Quantity[0.5, "SpeedOfLight"]}

How to solve formula f by using wolfram solver?