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Q.

The perimeter of the rectangle below is p inches and the area of the rectangle is 36 square inches. If l and w are integers, what is one possible value of p?

               t inches

                                                   w inches

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a

24

b

28

c

32

d

48 

answer is A.

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Detailed Solution

Concept- The perimeter P of a rectangle is given by the formula, Question Imagewhere l is the length of a rectangle and w is the width of a rectangle.
The area A of a rectangle is given by the formula, Question Imagewhere l is the length of a rectangle and w is the width of a rectangle.
               t inches                                                   w inches
   From the given figure, the length of the rectangle is l inches and breadth of the rectangle is w inches.
It is also given that the area of the rectangle is 36 square inches.
Question ImageAs we know that it has been given that both l and w are integers.
So, by using this information, we will find out the possible pairs ofQuestion Image.
The possible pairs of Question ImageAs we already know that the perimeter of rectangle is Question ImageBy substituting the possible pairs ofQuestion Image in the perimeter of rectangle, we get
Question ImageFrom the given options, only Question Imagematches the above possible set of values of p.
Hence, the correct answer is option (1).
 
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