Answer: [B}: " [tex]20a-2[/tex] " .
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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]: " [tex]20a -2[/tex] " .
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Hope this helps!
Best wishes to you in your academic endeavors
— and within the "Brainly" community!
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