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)
Answer: 6 cm x 8 cm