Question

alices backyard is a rectangular piece of property that is twice as long as it is wide. the total area of her yard is 1,000 m². what is the approximate width of her backyard?
a = lw
44.8 m
15.8 m
22.4 m
11.23 m

Explanation:

Step1: Definir variables

Sea la anchura \( w \), entonces la longitud \( l = 2w \).

Step2: Usar la fórmula del área

La fórmula del área de un rectángulo es \( A=lw \). Sustituyendo \( l = 2w \) y \( A = 1000 \), obtenemos \( 1000=(2w)w \).

Step3: Simplificar la ecuación

\( 1000 = 2w^{2} \), entonces \( w^{2}=\frac{1000}{2}=500 \).

Step4: Calcular la anchura

\( w=\sqrt{500}\approx22.4 \) (ya que \( \sqrt{484}=22 \), \( \sqrt{529}=23 \) y \( 500 \) está cerca de \( 484 \), \( \sqrt{500}\approx22.4 \)).

Answer:

C. \( 22.4\ m \)