SOLUTION: A rectangular lawn that is 1m by 3m in size is surrounded by a flowerbed of uniform width. the combined area of the lawn and flowerbed is 195m². what is the width of the flowerbed

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Question 1204761: A rectangular lawn that is 1m by 3m in size is surrounded by a flowerbed of uniform width. the combined area of the lawn and flowerbed is 195m². what is the width of the flowerbed
Found 2 solutions by math_tutor2020, greenestamps:
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

Refer to the diagram shown in my response here
https://www.algebra.com/algebra/homework/quadratic/Quadratic_Equations.faq.question.1197474.html
Use that as a template for this problem.

The inner rectangle is 1 meter by 3 meters.
The larger outer rectangle is 1+2x meters by 3+2x meters

The equation to solve is
(1+2x)(3+2x) = 195
I'll let you take over from here.

Hint: The answer is somewhere between 4 and 12.

Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


A quick and easy informal solution, if formal algebra is not required....

The difference between the two dimensions of the lawn is 2m, and the flower bed is of uniform width. That means the dimensions of the lawn plus flower bed differ by 2m.

So find two numbers whose difference is 2 and whose product is the given 195 square meters: 13m and 15m.

So adding the flower bed increases each dimension by 12m, which means the width of the flower bed is 6m.

ANSWER: 6m