Respuesta :

Answer:

[tex]\huge\red{\boxed{\blue{\boxed{\green{\boxed{13\: feet}}}}}}[/tex]

Step-by-step explanation:

to understand this:

you need to know about:

  • quadratic equation
  • solving quadratics
  • PEMDAS

tips and formulas:

  • area of rectangle=l×w

let's solve:

[tex]step - 1 : define[/tex]

[tex](x + 8)( x + 13) = 234[/tex]

[tex]step - 2 : slove[/tex]

  1. [tex] \text{simplify} : \\ x ^{2} + 21x + 104 = 234 [/tex]
  2. [tex] \text{cancel \:234 \: from \: both \: sides} : \\ {x}^{2} + 21x + 104 - 234 = 234 - 234 \\ {x}^{2} + 21x - 130 = 0[/tex]
  3. [tex] \text{rewrite \: 21x} : \\ {x}^{2} + 26x - 5x + 130 = 0[/tex]
  4. [tex] \text{factor\: out \: x} \: and \: - \text{5 \: respectively}: \\ {x}(x + 26) - 5(x + 26) = 0 [/tex]
  5. [tex] \text{factor \: out \: x - 5} : \\ (x - 5)(x + 26) = 0[/tex]
  6. [tex] x_{1} = 5 \\ x_{2} = - 26[/tex]

[tex] \therefore \: x = 5 \\ and \: the\: lenth \: of \: the \: rectangle \: is \: 5 + 8 = 13[/tex]

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