Question 1130566: The parks department is planning a new flower bed outside city hall. It will be rectangular with dimensions 9m by 6m. The flower bed will be surrounded by a path of constant width with the same area as the flower bed. Calculate the perimeter of the outside of the path.
a) set up a quadratic equation to model the situation
b) use the quadratic formula to solve the problem
im aware of the answer, however i am not sure how there is a 2 in the equation
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39613)   (Show Source):
You can put this solution on YOUR website! d, the size of the uniform width surrounding the garden.
The description means that the total garden path plus garden is TWICE the area of the garden. This is most likely the source of the "2" which you expect.
Solve the equation for d. Use whatever solution part makes sense.
Perimeter for the whole area will be 
Answer by ikleyn(52752)  (Show Source):
You can put this solution on YOUR website! .
You can easily solve this problem MENTALLY, without using equations.
The area of the flower bed is 9*6 = 54 square meters.
The flower bed surrounded by a path has the doubled area, i.e. 54*2 = 108 square meters.
This area is the product of the exterior dimensions L and W of the larger rectangle.
Notice, that the difference between L and W is the same as the difference of the dimensions of the flower bed -
exactly because the surrounding path has a constant width.
So, we need to find two numbers, whose product is 108 and whose difference is 3 = 9 - 6.
After 5 seconds thinking you will find these numbers: 12 and 9.
They are exterior dimensions.
From it, you need to make only one step to find the perimeter: it is 2*(12+9) = 42 meters.
Thus you get the answer: the perimeter is 42 meters.
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My other closely related lessons to it are the lessons
- Problems on the area and the dimensions of a rectangle surrounded by a strip
- Cynthia Besch wants to buy a rug for a room
- Problems on a circular pool and a walkway around it
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lessons are the part of this online textbook under the topic
"Dimensions and the area of rectangles and circles and their elements".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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