Aplaying card has a perimeter of 28 centimeters and an area of 48 square centimeters. what are the demensions of the card? show work! so much

Area (A) = Length (L) x width (w) and Perimeter (P) = 2L + 2w

P = 2L + 2w

28 = 2L + 2w substituted P with 28

14 = L + w divided both sides by 2

14 - L = w subtracted L from both sides

A = Lw

48 = L(14 - L) substituted A with 48 and "w" with "14 - L"

48 = 14L - L² distributed L into 14 - L

L² - 14L + 48 = 0 subtracted 14L and added L² to both sides

(L - 6)(L - 8) = 0 factored left side

L=6, L = 8 solved for L

A = Lw → 48 = 6w → 8 = w (similarly, plugging in L=8 will result in w=6)

6 cm x 8 cm

idk

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