A rectangular garden PQRS is divided into two rectangular beds by a straight path UV, where U is on PQ and V is on SR (so PUVS and UQRV are the two beds). H is a sprinkler point on PS, D is a sprinkler point on QR, and M is the midpoint of UV. The perimeter of PQRS is 84 m and PS : PQ = 3 : 4. Find (a) PS, and (b) the total area of the shaded triangles HMV and UMD.
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