Question 1208618
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Tutor @ikleyn has provided a response showing a good formal algebraic solution.<br>
Note in particular the algebraic "trick" she used: the sum of the length and width is 14; instead of using "x" and "14-x" for the two lengths, she used "7+x" and "7-x".  Doing that makes the algebra required to finish the problem easier.<br>
Of course, if formal algebra is not required, and if the speed of reaching the solution is important -- as on a timed competitive exam -- then a quick mental solution is simple.  The sum of the length and width is 14 and the product (the area) is 40, so you are looking for two numbers whose sum is 14 and whose product is 40.  Two seconds of thought (if you are slow!) gives the dimensions as 4 and 10.<br>