+84 we can solve this problem by looking at right triangle QVU. ST:PQ is 5:7. so QU is 7/12 of SQ. QV would be 7/12 of QR. the problem didn't give us QR or QS so we can make up values for them, because they would eventually cancel out. so ill set QR to 48, and QS would therefore be 52. after doing the calculations we get that QU is 91/3 and QV is 28. Applying the pythagorean thereom we get the UV is \(\boxed{\frac{35}{3}}\).
