Suppose the width is W cm.
Then length, L = 4W + 9.7
Therefore, perimeter = 2*(4W + 9.7 + W) = 2*(5W + 9.7) = 10W + 19.4 cm
That is, 10W + 19.4 cm = 91.4 cm
Therefore, 10W = 91.4 - 19.4 = 72.0 cm
and so W = 7.2 cm.
Then L = 4W + 9.7 = 38.5 cm.
The rectangle is 7.2 cm x 38.5 cm