Question

swbat - determine whether two quantities vary directly given a relationship represented graphically, numerically, algebraically, or verbally. do now: table with columns graph (with two graph images) and formula (first row: ( k=1.6m ); second row: ( m=0.6265k ), ( m=(1/1.6)k )) what do you notice? what do you wonder? part 1: measuring squares for each square, determine the side length and diagonal length. round each measurement to the nearest millimeter. two square diagrams (1 and 2) with blanks: 1. side length = ____; diagonal length = __ 2. side length = __; diagonal length = ____

Explanation:

To solve for the side length and diagonal length of a square, we can use the following steps:

For a square with side length \( s \):

1. Measure the side length: Use a ruler to measure the length of one side of the square. Let's assume we measure the first square (1.) and find the side length to be, for example, \( 10 \) millimeters (this will depend on the actual size of the square in the image).
2. Calculate the diagonal length: For a square, the diagonal \( d \) can be found using the Pythagorean theorem. In a square, the diagonal forms a right triangle with two sides, so \( d = s\sqrt{2} \). If \( s = 10 \) mm, then \( d = 10\sqrt{2} \approx 14 \) mm (rounded to the nearest millimeter).

Example for Square 1:

• Step 1: Measure Side Length

Suppose the side length (measured with a ruler) is \( 10 \) mm.
\( s = 10 \) mm

• Step 2: Calculate Diagonal Length

Using \( d = s\sqrt{2} \), substitute \( s = 10 \):
\( d = 10\sqrt{2} \approx 10 \times 1.414 \approx 14 \) mm

Example for Square 2:

• Step 1: Measure Side Length

Suppose the side length (measured with a ruler) is \( 15 \) mm.
\( s = 15 \) mm

• Step 2: Calculate Diagonal Length

Using \( d = s\sqrt{2} \), substitute \( s = 15 \):
\( d = 15\sqrt{2} \approx 15 \times 1.414 \approx 21 \) mm

Final Answers (Example Values):

1.
side length = \( \boldsymbol{10} \) mm
diagonal length = \( \boldsymbol{14} \) mm

2.
side length = \( \boldsymbol{15} \) mm
diagonal length = \( \boldsymbol{21} \) mm

(Note: Actual values will depend on the physical size of the squares in the image. Use a ruler to measure the side length accurately, then apply \( d = s\sqrt{2} \) to find the diagonal.)

Answer:

To solve for the side length and diagonal length of a square, we can use the following steps:

For a square with side length \( s \):

1. Measure the side length: Use a ruler to measure the length of one side of the square. Let's assume we measure the first square (1.) and find the side length to be, for example, \( 10 \) millimeters (this will depend on the actual size of the square in the image).
2. Calculate the diagonal length: For a square, the diagonal \( d \) can be found using the Pythagorean theorem. In a square, the diagonal forms a right triangle with two sides, so \( d = s\sqrt{2} \). If \( s = 10 \) mm, then \( d = 10\sqrt{2} \approx 14 \) mm (rounded to the nearest millimeter).

Example for Square 1:

• Step 1: Measure Side Length

Suppose the side length (measured with a ruler) is \( 10 \) mm.
\( s = 10 \) mm

• Step 2: Calculate Diagonal Length

Using \( d = s\sqrt{2} \), substitute \( s = 10 \):
\( d = 10\sqrt{2} \approx 10 \times 1.414 \approx 14 \) mm

Example for Square 2:

• Step 1: Measure Side Length

Suppose the side length (measured with a ruler) is \( 15 \) mm.
\( s = 15 \) mm

• Step 2: Calculate Diagonal Length

Using \( d = s\sqrt{2} \), substitute \( s = 15 \):
\( d = 15\sqrt{2} \approx 15 \times 1.414 \approx 21 \) mm

Final Answers (Example Values):

1.
side length = \( \boldsymbol{10} \) mm
diagonal length = \( \boldsymbol{14} \) mm

2.
side length = \( \boldsymbol{15} \) mm
diagonal length = \( \boldsymbol{21} \) mm

(Note: Actual values will depend on the physical size of the squares in the image. Use a ruler to measure the side length accurately, then apply \( d = s\sqrt{2} \) to find the diagonal.)