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lesya [120]
3 years ago
8

Si a los lados de un cuadrado se le aumenta en 3 y 5 m respectivamente la superficie del nuevo rectangulo es 440m .Encontrar el

lado del cuadrado inicial
Mathematics
1 answer:
Ivahew [28]3 years ago
3 0

Answer:

El lado del cuadrado inicial es 17 m.

Step-by-step explanation:

El área de un rectángulo se calcula a partir de los dos lados diferentes. Siendo a y b el valor de ambos lados, el área de la figura es el producto de los dos lados contiguos del rectángulo.

A los lados de un cuadrado se le aumenta en 3 y 5 m respectivamente la superficie del nuevo rectángulo es 440 m². Siendo x el lado del cuadrado inicial, entonces el área del rectángulo se puede expresar como:

(x+3)*(x+5)= 440 m²

Resolviendo:

x*x + 5*x + 3*X + 3*5= 440

x² + 8*x + 15=440

x² + 8*x + 15 -440= 0

x² + 8*x -425= 0

Una función cuadrática de la forma a*x² + b*x + c= 0 se puede resolver mediante la expresión:

\frac{-b+-\sqrt{b^{2}-4*a*c } }{2*a}

En este caso, a=1, b=8 y c=425. Reemplazando:

\frac{-8+-\sqrt{8^{2}-4*1*(-425) } }{2*1}

Resolviendo:

\frac{-8+\sqrt{8^{2}-4*1*(-425) } }{2*1}= \frac{-8+\sqrt{64+1700} }{2*1}= \frac{-8+\sqrt{1764 } }{2}= \frac{-8+42 }{2}= \frac{34}{2} = 17

y

\frac{-8-\sqrt{8^{2}-4*1*(-425) } }{2*1}= \frac{-8-\sqrt{64+1700} }{2*1}= \frac{-8-\sqrt{1764 } }{2}= \frac{-8-42 }{2}= \frac{-50}{2} = -25

Como las longitudes no pueden ser negativas, <u><em>el lado del cuadrado inicial es 17 m.</em></u>

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