Respuesta :

mhanifa

Answer:

  • 6 in and 15 in

Step-by-step explanation:

Given:

  • l = 2w + 3
  • A = 90 in²
  • w = ?
  • l = ?

Area formula:

  • A = lw

Substitute values and solve for w:

  • (2w+3)w = 90
  • 2w² + 3w = 90
  • 2w² + 3w - 90 = 0
  • w = (-3 ± [tex]\sqrt{3^2 - 4*2*(-90)}[/tex])/2*2
  • w = (-3 ± √729)/4
  • w = (-3 ± 27)/4
  • w = 6 (positive root only)

The width is 6 in, find the length:

  • l = 2*6 + 3 = 15 in

width be x

  • Length be 2x+3

Now

  • area=Length×Breadth
  • x(2x+3)=90
  • 2x²+3x=90
  • 2x²+3x-90=0

On solving we will get

  • x=6[Take positive]

Now

Length=2(6)=3=15in

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