Question

Which expression represents the perimeter of the figure in the diagram?

Answer 1

Answer:  [B}:  " $20a-2$ " .

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Step-by-step explanation:

The perimeter, "P", of the given quadrilateral [which is a trapezoid];  refers to the value of the sum of all the [Four (4) — in this case] side lengths of the given quadrilateral.  

Note that the all the [four (4)] side lengths are given.

The answer choices provided are "simplified expressions" that all contain one variable; which is— "a" .

Note that all side lengths of the figure have side lengths that contain one variable—which is— "a" .

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So, to calculate the perimeter, "P" :

Let us add up all the 4 (four) given side lengths of this quadrilateral:

P = (5a − 7) + (7a + 2) + (4a + 3) + (4a) ;

  = 5a − 7 + 7a + 2 + 4a + 3 + 4a  ;

Now, combined the "like terms" ; as follows:

     →   +5a + 7a + 4a + 4a ;

  =  (+5a + 7a) + 4a + 4a ;  

  = +12a + 4a + 4a ;

  = (+12a + 4a) + 4a ;

  =  (+16a) + 4a ;

  =  +20a ;

     →   − 7 + 2 + 3 ;

 =   − 5 + 3 ;

 =  − 2 ;

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And we have:

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 →   +20a − 2 ;  

 →  which is:  Answer choice:  [B]:  " $20a -2$ " .

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Hope this helps!

Best wishes to you in your academic endeavors

   — and within the "Brainly" community!

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Answer 2

Yo sup??

perimeter of the figure can be obtained by just adding all the sides

4a+4a+3+7a+2+5a-7

=20a-2

correct answer is option B

Hope this helps