SOLUTION: My garden measures 91 square feet. The length of the garden is one foot less than twice its width. What are the dimensions of the garden?

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Question 1179810: My garden measures 91 square feet. The length of the garden is one foot less than twice its width.
What are the dimensions of the garden?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52844)   (Show Source): You can put this solution on YOUR website!
.
x = the width

2x-1 = the length.


The area equation


    x*(2x-1) = 91.     (1)


Multiply it by 2


    2x*(2x-1) = 182.


     +-----------------------------------------------------------+
     |   Now ask yourself: which two consecutive integer numbers | 
     |            give 182 when multiplied ?                     |
     +-----------------------------------------------------------+



Think 3-4-5 seconds and guess the answer MENTALLY :  the numbers are 13 and 14.


CHECK:  13*14 = 182.      ! Correct !


So,  2x = 14 and x = 7.


The width is 7 cm.  The length is  13 cm.


Alternatively, you can solve equation (1) formally as a quadratic equation.


You will get the same answer.

Solved, answered, explained and completed.


Happy learning (!)



Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!


Mentally, in a few seconds....

91=13*7; 13 is 1 less than twice 7.

ANSWER: width 7 feet, length 13 feet

Or, if formal algebra is required, you can of course do something like the other tutor showed.
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