Question

1.2 perimeter of a square
your teacher will give you a picture of 9 different squares and ask your group to examine more closely.

1. for each of your assigned squares, measure the length of the diagonal and the perimeter of the square in centimeters. check your measurements with your group. after you reach an agreement, record your measurements in the table.

	diagonal (cm)	perimeter (cm)
square b
square c
square d
square e
square f
square g
square h
square i

1. plot the diagonal and perimeter values from the table on the coordinate - plane.
2. what do you notice about the points on the graph?

pause here so your teacher can review your work.

1. record measurements of the other squares to complete your table.

202 • grade 7

Explanation:

Step1: Recall square - related formulas

Let the side length of a square be $a$, the diagonal $d$, and the perimeter $P$. For a square, $d = \sqrt{2}a$ and $P=4a$. So, $a=\frac{d}{\sqrt{2}}$ and $P = 4\times\frac{d}{\sqrt{2}}=2\sqrt{2}d$.

Step2: Measure and record

Use a ruler to measure the diagonal of each square (in cm) and record it in the "diagonal (cm)" column of the table. Then, use the formula $P = 2\sqrt{2}d$ to calculate the perimeter for each square and record it in the "perimeter (cm)" column.

Step3: Plot the points

On the coordinate - plane, use the diagonal values as the $x$ - coordinate and the perimeter values as the $y$ - coordinate to plot the points for each square.

Step4: Analyze the points

The points on the graph should lie on a straight line. This is because the relationship between the diagonal $d$ and the perimeter $P$ of a square, $P = 2\sqrt{2}d$, is a linear relationship of the form $y = mx$ (where $y = P$, $x = d$, and $m = 2\sqrt{2}$).

Step5: Complete the table

Measure the diagonals of the remaining squares, calculate their perimeters using the formula $P = 2\sqrt{2}d$, and record the values in the table.

Answer:

1. Measure diagonals, calculate perimeters using $P = 2\sqrt{2}d$ and record.
2. Plot points with diagonal as $x$ - value and perimeter as $y$ - value.
3. Notice that the points lie on a straight line due to the linear relationship $P = 2\sqrt{2}d$.
4. Measure and record for remaining squares.