Question 587128: what are the dimensions of the lot if the perimeter is 19 meters and area of 21 square meters?
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! There are many word problems where you have to find two numbers when you are given their sum and their product. The wording may be different, but the strategy to solve them is the same. (See TIP below).
If we assume the lot is shaped like a rectangle (mine is not), we can write equations relating the perimeter, P, and the area, A, to the dimensions, x and y (length and with) of the lot.
 and  <--> <--> .
See how you were given the sum and the product of two numbers?
With the information given, we can write:
 or  or 
and 
See how you were given the sum and the product of two numbers?
Solving for y in the sum equation,
-->  ,
and substituting that expression into the product equation,
-->  ,
you could get to a quadratic equation:
-->  --> 
USEFUL TIP:
Or you could have been told that whenever you have the sum and the product of two numbers, the numbers can be found as the two solutions of the quadratic equation
Solving , or the equivalent equation that you get by multiplying both sides times 2,
 ,
you get the solutions  and  .
So the lot measures 6 meters by 3.5 meters.
NOTE:
I could expand on anything I stated, or explain anything further, but I know that I tend to over-explain and over-expand, so if you need expansion or explanation you'll have to ask. (If you use the website thank you note feature, to include questions, I'll be sure to see them, because the website sends me an automatic email. That email to me will include your email address, so I can answer you directly, but your email address will not be made available to anyone else. If, as I usually do, I answer you by email, you will know my email address too).
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