Question

1. determine the side length of each square.

a)
area = 484 mm²
b)
area = 1764 yd.²

Explanation:

Part a)

Step1: Recall area formula for square

The area \( A \) of a square is given by \( A = s^2 \), where \( s \) is the side length. We need to solve for \( s \) when \( A = 484 \, \text{mm}^2 \). So we take the square root of the area: \( s=\sqrt{A} \).

Step2: Calculate the square root

Substitute \( A = 484 \) into the formula: \( s=\sqrt{484} \). Since \( 22\times22 = 484 \), we have \( s = 22 \, \text{mm} \).

Part b)

Step1: Recall area formula for square

Again, use the area formula for a square \( A = s^2 \), where \( A = 1764 \, \text{yd}^2 \). We solve for \( s \) by taking the square root: \( s=\sqrt{A} \).

Step2: Calculate the square root

Substitute \( A = 1764 \) into the formula: \( s=\sqrt{1764} \). Since \( 42\times42=1764 \), we get \( s = 42 \, \text{yd} \).

Answer:

a) The side length of the square is \( \boldsymbol{22 \, \text{mm}} \).
b) The side length of the square is \( \boldsymbol{42 \, \text{yd}} \).