Question

Calcular las dimensiones de un rectángulo sabiendo que su perímetro es 94 cm. Y su area 352 cm^2

Answer 1

Respuesta:

Perimetro.

2a+2b.

2a=18.698056603830188566038018867132

2b=75.301943396169811433961981132868

2a+2b=94cm.

a=9.349028301915094283019009433566

b=37.650971698084905716980990566434.

Área.

axb.

axb=(9.349028301915094283019009433566)(37.650971698084905716980990566434)=352cm².

Explicación paso a paso:

2a+2b=94.

axb=352.

$a=\frac{352}{b}$

   $2(\frac{352}{b} )+2b=94.\\\\(\frac{704}{b})+2b=94.\\\\b(\frac{704}{b}+2b)=94(b)\\\\2b^{2}-94b+704\\\\\frac{2b^{2}-94b+704 }{2}\\\\b^{2}-47b+352$

Luego utilizamos la Fórmula general cuadrática,

$x=\frac{-b\±\sqrt[2]{b^{2}-4(a)(c)} }{2(a)}\\\\x=\frac{-(-47)\±\sqrt[2]{(-47)^{2}-4(1)(352)} }{2(1)}\\\\x=\frac{47\±\sqrt[2]{2,209-1,408} }{2}\\\\x=\frac{47\±\sqrt[2]{801} }{2}\\\\x=\frac{47\±28.30194339}{2}\\\\x_{1} =\frac{47+28.30194339}{2}\\\\x_{2} =\frac{47-28.30194339}{2}\\\\x_{1} =\frac{75.301943396169811433961981132868}{2}\\\\x_{2} =\frac{18.698056603830188566038018867132}{2}\\\\x_{1} =37.650971698084905716980990566434\\\\x_{2}=9.349028301915094283019009433566.$

Comprobación,

(b-37.650971698084905716980990566434)(b-9.349028301915094283019009433566)=$b^{2}-47b+352$.

(-37.650971698084905716980990566434b-9.349028301915094283019009433566b)=-47.

(-37.650971698084905716980990566434)(-9.349028301915094283019009433566)=352.