Answers:
Length = 46 meters
Width = 23 meters
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Work Shown:
Multiply the first coefficient (6) and the last term (-7) to get -42. We need to find factors of -42 that add to -19
Turns out that those two numbers are -21 and 2, which you find by trial and error.
-21 * 2 = -42
-21 + 2 = -19
Break up -19x as -21x+2x and use the factor by grouping method
6x^2 - 19x - 7
6x^2 - 21x + 2x - 7
(6x^2 - 21x) + (2x - 7)
3x(2x - 7) + 1(2x - 7)
(3x+1)(2x-7)
The factorization represents the length*width, since this product is equal to the rectangle's area.
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Plug x = 15 into each factor
3x+1 = 3*15+1 = 46
2x-7 = 2*15-7 = 23
The length and width are 46 and 23