The perimeter of parallelogram pqrs is 84. find the length of each side of pqrs when pq=qr and rs=sp-7

Step-by-step explanation:

Since all four sides of $PQRS$ are equal, $PQRS$ is a rhombus so that $\overline{PR}$ and $\overline{QS}$ are perpendicular bisectors of each other. Let $\overline{PR}$ and $\overline{QS}$ intersect at $M$.

[asy] unitsize(1 cm); pair A, B, C, D, M; A = (0,1); B = (2,0); C = (0,-1); D = (-2,0); draw(A--B--C--D--cycle); draw(A--C); draw(B--D); label("$P$", A, N); label("$Q$", B, E); label("$R$", C, S); label("$S$", D, W); label("$M$", M, NE); [/asy]

Then $PM=7$ and $QM=24$, so that $PQ=25$ by Pythagorean theorem. Hence, the perimeter of $PQRS$ is $4 \cdot 25 = \boxed{100}$.

b

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