let

l = the length of the rectangle

w = the width of the rectangle

the area A = 156 cm^2

A = l*w

l*w = 156

the perimeter P = 50 cm

2(l + w) = 50 divide both sides by 2

l + w = 25

l = 25 - w

plug l = 25 - w into l*w = 156

(25 - w)w = 156

by solving we find 2 solutions

w1 = 13 cm

w2 = 12 cm

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for w1 = 13 the length l1 = 25 - 13 = 12 cm

for w2 = 12 cm the length l2 = 25 - 12 = 13 cm

the dimensions of the rectangle are 12 cm and 13 cm.