the area of a rectangle is 21 in^2. the length is 2 times the width plus one

Answer 1

W = width

L = length

L = 2W + 1

Area = 21 sq in

Area = L * W

Area = (2W + 1)*W

21 = 2W² + 1W

2W² + 1W - 21 = 0

Solve with the quadratic equation with a = 2 b = 1 and c = -21

Let W = x

x = -1 +/- square root of (1 - 8(-21))

4

x = -1 +/- square root of 169

4

x = -1 +/- 13

4

x = (-1 + 13) / 4

x = (-1 - 13) / 4

x = 3 and -14/4

x represents the Width of the rectangle and W cannot be negative.

So W = 3 and L = 2W + 1

L = 2*3 + 1 = 7

The rectangle has a Width of 3 inches and a Length of 7 inches.

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Answer 2

Length = 7 and width = 3