Question 1057349
Let l = length
Let w = width

Need to find l and w.  Two unknowns so look for two equations.

(1)  l = w+12   ("length is 12cm longer than its width")
(2)  2l + 2w = 84   ("perimeter is 84cm")

...
Eq (1) allows us to subs "w+12" for "l" in (2):

    2(w+12) + 2w = 84    (eq (2) w/substitution made)
     2w + 24 + 2w = 84    (multiplied 2 into parens)
        4w + 24 = 84         (combined like terms)        
        4w = 60                  (subtracted 24 from both sides)
          w = 60/4               (divided both sides by 4)
          w = 15cm

From (1),  l = 15+12 = 27cm
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Ans:   The rectangle has dimensions 27cm x 15cm
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Check:
  We can plug into (2) to check:
        2(27) + 2(15) = 54 + 30 = 84  (ok)