Problema Solution
Originally a rectangle was twice as long as it was wide. When 4 m were added to its length and 3 m subtracted from it's width, the resulting rectangle had an area of 600 m^2. Find the dimensions of the new rectangle.
Answer provided by our tutors
let
l = the length of the original rectangle, l>0
w = the width of the original rectangle, w>0
l + 4 = the length of the new rectangle
w - 3 = the width of the new rectangle, w - 3>0 or w>3
Originally a rectangle was twice as long as it was wide:
l = 2w
the resulting rectangle had an area of 600 m^2:
(l + 4)(w - 3) = 600
plug l = 2w into the last equations:
(2w + 4)(w - 3) = 600
by solving we find:
w = 18 m
w - 3 = 18 - 3 = 15 m
l = 2*18
l = 36 m
l + 4 = 36 + 4 = 40 m
the dimensions of the new rectangle are: the length is 40 m and the width is 15 m.