Question 744252

A rectangle is 5m longer than it is width . If the length is shortened by 2 meters and the width is increased by 1 m. The area will remain the same. Find the length and width.

Your answer would be highly appreciated. Thank you!


Let original width be W


Then length = W + 5


Original area = W(W + 5), or {{{W^2 + 5W}}}


Shortened by 2 meters, the new length is: W + 5 - 2, or W + 3


Increased by 1, the new width is: W + 1


New area = (W + 3)(W + 1), or {{{W^2 + 4W + 3}}}


Since area remains the same, then: {{{W^2 + 5W = W^2 + 4W + 3}}}


{{{W^2 - W^2 + 5W - 4W = 3}}} 


W, or original width = {{{highlight_green(3m)}}}


Original length = 3 + 5, or {{{highlight_green(8m)}}}


You can do the check!!


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