Question

1. find the length of a side of a square if its area is:

a. 81 square inches
b. \\(\frac{4}{25}\\) cm² (with a hand - drawn square, notes: \\(\frac{2}{5}\times\frac{2}{5}=\frac{4}{25}\\), and \\\(l\times w\\)\ with \\(\frac{2}{5}\\) labeled)
c. 0.49 square units
d. \\(m^2\\) square units

Explanation:

Part a: Area = 81 square inches

Step1: Recall the formula for the area of a square.

The area \( A \) of a square with side length \( s \) is given by \( A = s^2 \). To find the side length, we need to solve for \( s \), so \( s=\sqrt{A} \).

Step2: Substitute the given area into the formula.

Given \( A = 81 \) square inches, then \( s=\sqrt{81} \).

Step3: Calculate the square root.

We know that \( 9\times9 = 81 \), so \( \sqrt{81}=9 \).

Step1: Use the area formula for a square.

For a square, \( A = s^2 \), so \( s=\sqrt{A} \).

Step2: Substitute the area value.

Given \( A=\frac{4}{25} \) \( \text{cm}^2 \), then \( s = \sqrt{\frac{4}{25}} \).

Step3: Simplify the square root.

We know that \( \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}} \) (for \( a\geq0,b > 0 \)). So \( \sqrt{\frac{4}{25}}=\frac{\sqrt{4}}{\sqrt{25}} \). Since \( \sqrt{4} = 2 \) and \( \sqrt{25}=5 \), we have \( \frac{2}{5} \).

Step1: Recall the square's area formula.

\( A=s^2\), so \( s = \sqrt{A} \).

Step2: Substitute the area.

Given \( A = 0.49 \) square units, then \( s=\sqrt{0.49} \).

Step3: Calculate the square root.

We know that \( 0.7\times0.7=0.49 \), so \( \sqrt{0.49} = 0.7 \).

Answer:

The length of the side is 9 inches.

Part b: Area = \(\frac{4}{25}\) \( \text{cm}^2 \)