Exercise 33 Page 795

a We are asked to redraw a kite with diagonals of

12

cm and

4

cm. To do this let's start with drawing a horizontal diagonal

A C

that has a length of

12

cm.

Next, as we want the point of intersection of the diagonals to be $2$ cm from point $A,$ we will draw a segment $B D$ that is perpendicular to $A C$ and satisfy this condition. Notice that we are given that the second diagonal has a length of $4$ cm and in a kite one diagonal bisects the other.

Finally we can connect the vertices to form a kite $A B C D .$

b In this part we are asked to draw four more kites, but each time with different value of

x .

Let's choose

x = 4,

6,

8,

and

10 .

We will name the vertices with consecutive letters.

c Now we will measure and record in a table the perimeter of each kite we draw, along with the

x -

value.

Kite	$x$	Perimeter
$A B C D$	$2$	$\approx 26.1$
$E F G H$	$4$	$\approx 25.4$
$I J K L$	$6$	$\approx 25.3$
$M N O P$	$8$	$\approx 25.4$
$Q R S T$	$10$	$\approx 26.1$

d In this part we will graph the perimeter versus the

x -

value using the data from the table we made in the previous part. Perimeter will be on the vertical axis and the

x -

values will be on the horizontal axis.

e Looking at the graph we made in Part D, we can assume that the perimeter will be minimized for

x = 6 .

It is a significant conclusion because for

x = 6

the diagonals bisect each other and the figure is a rhombus.

Subchapter links

Check Your Understanding p.793

H.O.T. Problems p.795

Standardized Test Practice p.796

Spiral Review p.796

Skills Review p.796