1- The width of the rectangular painting is 2 in. less than the length. The area is 120 in^2. Find the length and width.

[img width="229" height="74" src="file:///C:/Users/guest/AppData/Local/Temp/msohtmlclip1/01/clip_image001.png" v:shapes="Rectangle_x0020_1">

X X-2

Area of Rectangle = Length * Width

This implies that

X * (X-2) = 120

Expand the equation

X^2 - 2x = 120

X^2 - 2x - 120 = 0

Solving by factorization

X^2 - 12x + 10x -120 = 0

Factorize

X(X - 12) 10(X- 12) = 0

Combine

(X+10) (X-12) = 0

Therefore:

X=-10 or X=12

Since we cannot have a negative value for length ‘x’

X= 12

If the Length X= 12, then the Width = (12-2)=10

Check:

Length * Width = 120

12 * 10 = 120

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