Respuesta :

alinateow
let the width be : x
length : (2x - 6)

(2x - 6) (x) = 2x square - 6x

2x square - 6x = 140
2x square - 6x - 140 = 0

if you use the cross method or calculator you’ll get :

( x - 10 ) ( x + 7) = 0

x = 10 or x = -7 ( reject because negative )
so we use x = 10.

width = 10
length = 2(10) - 6 = 14

Eduard22sly

The dimensions of the tennis court are:

Length = 14 m

Length = 14 mWidth = 10 m

Let the width be y.

From the question given above,

The length is 6 meters less than twice it’s width. This can be obtained written as:

Length = 2y – 6

Area = 140 m²

Dimension =?

  • Next, we shall determine the width (i.e y)

Dimension = Area = Length × width

140 = (2y – 6)y

140 = 2y² – 6y

Rearrange

2y² – 6y – 140 = 0

Divide through by 2

y² – 3y – 70 = 0

  • Multiply the 1st term (i.e y²) and the last term (i.e –70) together.
  • The result is –70y². Find two factors of –70y² such that their sum will result to the 2nd term (i.e –3y).
  • The factors are –10y and 7y.
  • Substitute –10y and 7y in place of –3 in the equation above.

y² – 3y – 70 = 0

y² – 10y + 7y – 70 = 0

Factorize

y(y – 10) + 7(y – 10) = 0

(y – 10)(y + 7) = 0

y – 10 = 0 or y + 7 = 0

y = 10 or –7

Since measurement can not be negative,

Width = y = 10 m

  • Finally, we shall determine the length.

Length = 2y – 6

y = 10

Length = 2(10) – 6 = 20 – 6

Length = 14 m

Therefore, the dimensions of the tennis court are

Length = 14 m

Length = 14 mWidth = 10 m

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