A person has a garden that has a length 10 feet longer than the width. Set up a quadratic equation
to fi d the dimensions of the garden if its area is
119 ft.2. Solve the quadratic equation to fi d the
length and width.

The width is 7 ft

The length is 17 ft

Step-by-step explanation:

width = w

length = w+10

A = l*w

119 = w*(w+10)

Distribute

119 = w^2 + 10 w

Subtract 119 from each side

0 = w^2 +10w-119

Factor

0 = ( w-7) (w+17)

Using the zero product property

0 = w-7     0 = w+17

w = 7       w = -17

Since the width cannot be negative

w =7

l = w+10

l = 17

The width is 7 ft

The length is 17 ft

Quadratic equation:   x² + 10x - 119 = 0

  Length:   17 feet

    Width:     7 feet

Step-by-step explanation:

length:  x + 10

width:  x

Area = Length * Width

119 = (x + 10) * x

119 = x² + 10x

x² + 10x - 119 = 0

x² + 10x - 119 = (x + 17)(x - 7) = 0

x + 17 = 0 and x - 7 = 0

      x = -17  and  x = 7

Positive length and width makes more sense...

  length:  -17 + 10 = -7

   width:  -17

  length:  7 + 10 = 17

    width:  7

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step-by-step explanation: