The length of a rectangle is 3 inches longer than half of its width. The area of the rectangle is 416 square inches. How many inches in width is the rectangle?

Width = 26 inches

Step-by-step explanation:

The area of the rectangle is:

area = (length*width)

416 = a*b

a = b/2  + 3

a = length

b = width

then:

416 = (b/2 + 3) (b)

416 = b*b/2 + b*3

416 = b²/2 + 3b

0 = b²/2 + 3b - 416

b = {-(+3)±√((3²)-(4*1/2*-416))} / (2*1/2)

b = {-3±√(9+832)} / 1

b = {-3±√841}

b = -3±29

only take the positive value becuse is a natural number

b = -3+29

b = 26 inches

a = b/2 + 3

a = 26/2 + 3

a = 13 + 3

a = 16 inches

Check:

416 = 16 * 26  

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