Question

1. connie is planning a square patio which must have an area of 22 square yards. a. what is the best estimate for the patios side length to the nearest hundredth? b. connie only has a yard - stick with her. it is marked in one - inch increments, so each increment is 1/36 of a yard. after measuring full yards, which mark on the yard - stick is closest to the remaining side length of the patio?

Explanation:

Step1: Recall area - side relationship for square

For a square, the area formula is $A = s^{2}$, where $A$ is the area and $s$ is the side - length. Given $A = 22$ square yards, we need to find $s$. So, $s=\sqrt{A}=\sqrt{22}$.

Step2: Calculate the square - root

Using a calculator, $\sqrt{22}\approx4.69$ yards.

for part b:
We know that $1$ yard = 36 inches. Let the side - length of the patio be $s = 4.69$ yards. First, convert the side - length to inches: $4.69\times36=168.84$ inches. After measuring full yards (4 yards), the number of full yards is 4, and the remaining length in yards is $4.69 - 4=0.69$ yards. Convert $0.69$ yards to inches: $0.69\times36 = 24.84$ inches. Since the yard - stick is marked in one - inch increments, the closest mark on the yard - stick to the remaining side - length is 25 inches.

Answer:

a. The best estimate for the patio's side - length to the nearest hundredth is $4.69$ yards.