let

l = the length of the rectangle

w = the width of the rectangle

the perimeter of the rectangle is 42 cm

2(l + w) = 42 divide both sides by 2

l + w = 21

l = 21 - w

the area is 68 cm^2

l*w = 68

plug l = 21 - w into l*w = 68

(21-w)*w = 68

by solving we find two roots

w1 = 17

w2 = 4

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for w = 17 we have l = 21-17 = 4

for w = 4 we get l = 21-4 = 17

since l>w the solution is l=17 cm and w=4 cm.