Question 1207411: Dimensions of a Window The area of a rectangular window is to be 306 square centimeters. If the length exceeds the width by 1 centimeter,what are the dimensions?
Let me see.
Area = 306
Length = x + 1
Width = x
My set up:
306 = x(x + 1)
Yes?
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3816)   (Show Source):
You can put this solution on YOUR website!
Good start so far.
The equation you wrote can be turned into x^2+x-306 = 0
From here use the quadratic formula, complete the square, or you can guess-and-check your way to factoring.
Hint: The answer is between 10 and 20.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
For a formal algebraic solution, your setup is fine.
If this is a question on a timed competitive exam, where the speed of answering the question is important, formal algebra is much too slow.
The question says that 306 is the product of two numbers whose difference is 1. Use any of a number of different mental methods to find that the two numbers are 17 and 18.
One quick mental method....
306 is between 100 and 400, so the two numbers are in the teens.
A final digit of 6 when multiplying two consecutive integers means the final digits of the two integers are either 2 and 3, or 7 and 8; 12 times 13 is way too small, so it must be 17 and 18.
Another mental method....
306 is between 17^2 = 289 and 18^2 =324, so the two consecutive integers have to be 17 and 18.
Presumably you were asked for a formal algebraic solution. However, note that practice in finding answers for problems like this mentally is good mental exercise.
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