Question

1. a square serving platter has an area of 124 in². which is the best estimate of one side length of the platter?

a. 31 inches
b. 11.6 inches
c. 11.8 inches
d. 11.1 inches

Explanation:

Step1: Recall area formula for square

The area formula for a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 124$ in², we need to find $s=\sqrt{A}=\sqrt{124}$.

Step2: Find perfect - square approximations

We know that $11^{2}=121$ and $12^{2}=144$. Since $124$ is closer to $121$ than to $144$.

Step3: Calculate approximate value

$\sqrt{121} = 11$ and $\sqrt{144}=12$. $\sqrt{124}$ is slightly greater than $11$. Calculate the differences: $124 - 121=3$ and $144 - 124 = 20$.
We can estimate $\sqrt{124}\approx11.1$ (by considering the relative proximity to $121$).

Answer:

D. 11.1 inches