Question

1. reid is building a fence around a square portion of his yard with an area of 200 square feet. which point below best represents the side length of one side of the fence? image of a number line with points a, b, c, d at various positions: a near 13-14, b near 14, c near 16-17, d at 20

Explanation:

Step1: Recall area of square formula

The area \( A \) of a square is given by \( A = s^2 \), where \( s \) is the side length. We know \( A = 200 \) square feet, so we need to solve for \( s \): \( s=\sqrt{200} \).

Step2: Simplify \( \sqrt{200} \)

Simplify \( \sqrt{200} \): \( \sqrt{200}=\sqrt{100\times2} = \sqrt{100}\times\sqrt{2}=10\sqrt{2}\approx10\times1.414 = 14.14 \)? Wait, no, wait: Wait, \( 14^2 = 196 \), \( 15^2=225 \). Wait, no, I made a mistake. Wait, \( 14^2 = 196 \), \( 15^2 = 225 \), but \( 200 \) is between \( 14^2 \) and \( 15^2 \)? No, wait, no: Wait, \( 14^2 = 196 \), \( 15^2 = 225 \), but \( \sqrt{200}\approx14.14 \)? Wait, no, that can't be. Wait, no, wait, the number line has 13,14,15,16,17,18,19,20,21. Wait, maybe I miscalculated. Wait, \( 14^2 = 196 \), \( 15^2 = 225 \), so \( \sqrt{200} \) is between 14 and 15? But the number line has points at A (around 13.5), B (around 14.1), C (16.5), D (20). Wait, no, wait, no, I think I messed up. Wait, no, the area is 200, so side length is \( \sqrt{200}\approx14.14 \), which is close to point B (which is at 14, a bit after 14). Wait, but let's recalculate: \( 14^2 = 196 \), \( 14.1^2 = 198.81 \), \( 14.2^2 = 201.64 \). So \( \sqrt{200}\approx14.14 \), which is between 14 and 15, closer to 14. So on the number line, point B is at 14 (a bit after 14), which matches \( \sqrt{200}\approx14.14 \). Wait, but let's check again. Wait, the number line: A is before 14, B is at 14 (maybe 14.1), C is 16.5, D is 20. So the side length is \( \sqrt{200}\approx14.14 \), so the point closest is B.

Wait, but wait, maybe I made a mistake. Wait, no, the area of the square is 200, so side length is \( \sqrt{200} \approx 14.14 \), which is represented by point B (since B is at 14, a bit after 14). So the correct point is B.

Answer:

B (the point labeled B, around 14 on the number line)