math area word problems?

Question

A rectangle is three times as long as it is wide.If its lenght and width are both decreased by 2cm, its area id decreased by 36cm2.Find its orginal dimensions.

ii'm so lost. please show work so i can figure out to do the rest of my work

Answer 1

L = 3W
A = LW = 3W^2
A - 36 cm^2 = (L - 2cm)(W - 2cm)
3W^2 - 36 cm^2 = (3W - 2cm)(W - 2cm)
3W^2 - 36 cm^2 = 3W^2 - 8W + 4 cm^2
-36 cm^2 = - 8W + 4 cm^2
36 cm^2 = 8W - 4 cm^2
8W = 40 cm^2
W = 5 cm
L = 15 cm

Answer 2

okay so start by the formula for the are of a rectangle, which is length times width right? or we'll call length "L" and width "W"
but the length they say is 3 times the width

so (3w) x (w) = A(area)
now you also know that
(3w-2)x(w-2) = A-36 (as was given in the question)

so 3w^2 = 3w^2 - 8w +40 (because they're both = to A)

so
-8w+40= 0
-8w = -40
w=5

so the original width of the rectangle, is 5.
so you substitute that into the original 3w^2 and you get 75 as your answer.

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