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Hi there! Have questions about your homework? At Brainly, there are 60 million students who want to help each other learn. Questions are usually answered in less than 10 minutes. Try it for yourself by posting a question! :D

Area of a rectangle is defined by the formula A = l x w and perimeter by the formula P = 2l + 2w ------------- given that area is 84 and perimeter is 38, you can substitute it to both equations stated above ---------- you'll have A = l x w 84 = l x w ----equation 1 P = 2l + 2w 38 = 2l + 2w ----equation 2 ------------ divide equation2 by 2 (38 = 2l + 2w) ÷ 2 19 = l + w l = 19 - w -----equation 3 ------------ substitute equation 3 to equation 1 84 = l (w) 84 = (19-w)(w) 84 = 19w -w^2 transpose 19w - w^2 to the left side of the equation w^2 - 19w + 84 = 0 factor (w-12)(w-7) = 0 w-12=0 w=12 w-7=0 w=7 -------- if w=12 substitute to equation 3 l = 19 - w l = 19 - 12 l = 7 ----------- if w=7 l = 19-w l = 19-7 l = 12 ---------- but common knowledge will tell you that length must be of greater value than the width. then you can say that l = 12 w = 7