Question

select the correct answer from each drop - down menu. the area of a square mat is 125 square inches. the best approximation of its length is inches. if the length of each side is increased by another inch, the area would increase by approximately square inches.

Explanation:

Step1: Find the side - length of the original square

The area formula of a square is $A = s^2$, where $A$ is the area and $s$ is the side - length. Given $A = 125$ square inches, then $s=\sqrt{A}=\sqrt{125}\approx11.18$ inches.

Step2: Calculate the increase in area

The new side - length $s'=s + 1=\sqrt{125}+1$. The new area $A'=(s + 1)^2=s^2+2s + 1$. The increase in area $\Delta A=A' - A=(s^2+2s + 1)-s^2=2s + 1$. Substitute $s=\sqrt{125}\approx11.18$ into the formula, we get $\Delta A\approx2\times11.18+1 = 23.36\approx23$ square inches.

Answer:

1. For the first blank: $\sqrt{125}\approx11.18$ inches.
2. For the second blank: Let the side - length of the original square be $s = \sqrt{125}$ inches. The new side - length is $s'=\sqrt{125}+1$ inches. The original area $A = 125$ square inches, and the new area $A'=(\sqrt{125}+1)^2=125 + 2\sqrt{125}+1$. The increase in area $\Delta A=A' - A=2\sqrt{125}+1\approx2\times11.18 + 1=22.36+1 = 23.36\approx23$ square inches.