Question

el perimetro de un rombo es 104 cm. Si su diagonal menor mide 20 cm, ¿cual es su area?

Answer 1

Respuesta:

        $480cm^{2}$

Explicación paso a paso:

$Perimetro: P = 104cm$

$Diagonal -menor: d = 20cm$

$Lado: L = ?$

Diagonal mayor: D = ?

$P = L+L+L+L = 4L$

$104cm = 4L$

$L = \frac{104cm}{4}$

$L = 26cm$

Por Pitágoras:

$L^{2} = (\frac{D}{2} )^{2} + (\frac{d}{2} )^{2}$

$(26cm)^{2} =(\frac{D}{2} )^{2} + (\frac{20cm}{2} )^{2}$

$676cm^{2} = \frac{D^{2} }{4} + 100cm^{2}$

$\frac{D^{2} }{4} = 676cm^{2} -100cm^{2}$

$D^{2} = 4(576)cm^{2}$

$D = \sqrt{2304cm^{2} }$

$D = 48cm$

$Area: A = ?$

$A = \frac{D*d}{2}$

$A = \frac{(48cm)*(20cm)}{2} = \frac{960cm^{2} }{2}$

$A = 480cm^{2}$