We would do best to begin with a picture.

One of our diagonals is bisected by the other, and thus each half is 12.  The other important thing to recall is that the diagonals of a kite are perpendicular.  Therefore we have four right triangles.  We can then use the Pythagorean Theorem to calculate the upper portion of the vertical diagonal to be 5.  That means that the bottom portion of our diagonal is 9.

Using the Pythagorean Theorem, we can calculate our remaining sides to be 15.

To find the missing side of this kite, work backwards using the formula:

\(\displaystyle p=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) represent the length of one side from each of the two pairs of adjacent sides. 

The solution is:

\(\displaystyle 26=2(6+b)\)

\(\displaystyle \frac{26}{2}=(6+b)\)

\(\displaystyle 13=6+b\)

\(\displaystyle b=13-6=7\)

To find the missing side of this kite, work backwards using the formula:

\(\displaystyle p=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) represent the length of one side from each of the two pairs of adjacent sides. 

The solution is:

\(\displaystyle 50=2(12+b)\)

\(\displaystyle \frac{50}{2}=12+b\)

\(\displaystyle 25=12+b\)

\(\displaystyle b=25-12=13\)

To find the missing side of this kite, work backwards using the formula:

\(\displaystyle p=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) represent the length of one side from each of the two pairs of adjacent sides. 

The solution is:

\(\displaystyle 34=2(14+b)\)

\(\displaystyle \frac{34}{2}=14+b\)

\(\displaystyle 17=14+b\)

\(\displaystyle b=17-14=3\)

To find the missing side of this kite, work backwards using the formula:

\(\displaystyle p=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) represent the length of one side from each of the two pairs of adjacent sides. 

The solution is:

\(\displaystyle 58=2(11+b)\)

\(\displaystyle \frac{58}{2}=11+b\)

\(\displaystyle 29=11+b\)

\(\displaystyle b=29-11=18\)

To find the missing side of this kite, work backwards using the formula:

\(\displaystyle p=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) represent the length of one side from each of the two pairs of adjacent sides. 

The solution is:

\(\displaystyle 2.5 feet=2(0.5 foot+b)\)

\(\displaystyle \frac{2.5}{2}=(0.5+b)\)

\(\displaystyle 1.25=0.5+b\)

\(\displaystyle b=1.25-0.5=0.75=\frac{3}{4}\)

To find the missing side of this kite, work backwards using the formula:

\(\displaystyle p=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) represent the length of one side from each of the two pairs of adjacent sides. 

The solution is:

\(\displaystyle 62=2(8+b)\)

\(\displaystyle \frac{62}{2}=(8+b)\)

\(\displaystyle 31=8+b\)

\(\displaystyle b=31-8=23\)

To find the missing side of this kite, work backwards using the formula:

\(\displaystyle p=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) represent the length of one side from each of the two pairs of adjacent sides. 

The solution is:

\(\displaystyle 138=2(33+b)\)

\(\displaystyle \frac{138}{2}=33+b\)

\(\displaystyle 69=33+b\)

\(\displaystyle b=69-33=36\)

To find the missing side of this kite, work backwards using the formula:

\(\displaystyle p=2(a+b)\), where \(\displaystyle a\) and \(\displaystyle b\) represent the length of one side from each of the two pairs of adjacent sides. 

The solution is:

\(\displaystyle 30=2(9.5+a)\)

\(\displaystyle 30=19+2a\)

\(\displaystyle 2a=30-19=11\)

\(\displaystyle a=\frac{11}{2}=5.5\)

The sides have the ratio \(\displaystyle 4:1\), thus the longer sides must be \(\displaystyle 4\) times greater than the smaller sides.

Since the longer sides are \(\displaystyle 12\) cm, the shorter sides must be: 

\(\displaystyle 12\div4=3\)