SOLUTION: LEARNING ACTIVITY: Solve the Inequality! INSTRUCTIONS: Read and analyze the real-life problems. Perform the task by following the solving steps and answer the questions that follow

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Question 1186519: LEARNING ACTIVITY: Solve the Inequality! INSTRUCTIONS: Read and analyze the real-life problems. Perform the task by following the solving steps and answer the questions that follow. Brendan is a Plantito who has 48 m of fencing materials. He wants to make a garden whose area is greater than 108 m² but less than 150 m². Find the possible dimensions of his garden. How many possible garden can he make that Quadratic Inequalities.​
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let x be one side of the rectangular garden, in meters.

Then the other (adjacent) side length is  48/2 - x = 24 - x meters long.


The expression for the area is  x*(24-x)  square meters.


The inequality, which you want to impose on dimensions (on the area) is


    108 <= x*(24-x) <= 150  square meters,


or, which is the same


    108 <= -x^2 + 24x <= 150.


The quadratic function  -x^2 + 24x  has the maximum value of 144, which is achieved at x = 12.

It is less than 150, so inequality  x^2 + 24x <= 150  is valid for ANY VALUE of x, without restrictions.



The inequality  108 <= -x^2 + 24x  is valid at  6 <= x <= 18.



So, one side of the rectangular garden MUST SATISFY this restrictions.


The other (adjacent) side should be (24-x) meters long.


    (By the way, then the other (adjacent) side satisfies the same restrictions/inequalities (!) )


There are INFINITELY MANY possibilities under these conditions.

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Solved.