Q17. - Algebra 1

Question

The function $s=\sqrt{A}$ can be used to find the length of a side of a square given its area. Use this function to determine the length of a side of a square with an area of 90 square inches. Round to the nearest tenth if necessary.

Step-by-Step Solution

Answer

The length of a side of a square with an area of 90 square inches rounded to the nearest tenth is 9.5 inches.

Step 1. Write the relationship between the length of a side of a square and the area of the square.

The relationship between the length of a side of a square and the area of the square is:

$s=\sqrt{A}$, where s is the length of a side of a square and A is the area of the square.

Step 2. Determine the length of a side of a square.

It is given that the area of the square is 90 square inches. Therefore, the value of A is 90.

Substitute 90 for A in $s=\sqrt{A}$.

$$\begin{gathered} s=\sqrt{A} \\ =\sqrt{90} \\ =\sqrt{9\times 10} \\ =\sqrt{3^2\times 10} \\ =3\sqrt{10} \\ =3\left(3.16227766\right) \\ =9.48683298 \\ \approx 9.5 \end{gathered}$$

Step 3. Conclusion

Therefore, the length of a side of a square with an area of 90 square inches rounded to the nearest tenth is 9.5 inches.