Question

The area of a rectangle is represented by 12n^2 - 19n – 21. If the width is 3n - 7, which expression represents the perimeter?

A. 7n - 4
B. 7n + 4
C. 14n - 8
D. 14n + 8
pls help!!!

Answer 1

C 14n - 8

Explanation:

area of rectangle = length × width = 12n² - 19n - 21

width = 3n - 7

so, what do we need to multiply with width to get the expression of the area ?

4n + 3

(because we think, what do we need to multiply 3n with to get 12n², and what to multiply -7 to get -21)

control : (3n-7)×(4n+3) = 12n²-28n+9n-21 = 12n²-19n-21

perimeter is now 2× length + 2× width

p = 2(3n-7) + 2(4n+3) = 6n - 14 + 8n + 6 = 14n - 8