Question

a homeowner has a square backyard with an area of 150 square feet. what is the length of one side of the backyard? select all answer choices that are true. a. the side length is between 11 and 12. b. the side length is between 12 and 13. c. the exact side length is $sqrt{150}$. d. the exact side length is 12.2 feet. e. the side length is $25sqrt{6}$. f. the side length is $5sqrt{6}$.

Explanation:

Step1: Usar fórmula del área de un cuadrado

Sabemos que el área $A$ de un cuadrado es $A = s^{2}$, donde $s$ es la longitud del lado. Dado que $A = 150$ pies cuadrados, entonces $s=\sqrt{150}$.

Step2: Simplificar la raíz cuadrada

$\sqrt{150}=\sqrt{25\times6}=5\sqrt{6}$.

Step3: Aproximar el valor de la raíz cuadrada

Calculamos $\sqrt{150}$. Sabemos que $12^{2}=144$ y $13^{2}=169$. Como $144<150<169$, entonces $\sqrt{144}<\sqrt{150}<\sqrt{169}$, es decir, $12 < \sqrt{150}<13$.

Answer:

C. The exact side length is $\sqrt{150}$.
F. The side length is $5\sqrt{6}$.
B. The side length is between 12 and 13.