This problem provides the lengths of the two perpendicular interior diagonal lines in the rhombus. To use this information to find the length of one side of the rhombus, apply the formula:  

\(\displaystyle s=\frac{\sqrt{a^2+b^2}}{2}\)

where \(\displaystyle s=\) the length of one side, and both \(\displaystyle a\) and \(\displaystyle b\) each represent one of the perpendicular diagonal lines. 

The solution is: 

\(\displaystyle s=\frac{\sqrt{5^2+12^2}}{2}=\frac{\sqrt{25+144}}{2}=\frac{\sqrt{169}}{2}=\frac{13}{2}=6.5\)

To solve this problem, apply the perimeter formula for a rhombus: \(\displaystyle P=4S\). 
Note that the perimeter formula for a rhombus is the same formula used to find the perimeter of a square. This is because both shapes, by definition, have \(\displaystyle 4\) equivalent sides. The total perimeter is the sum of all \(\displaystyle 4\) sides. 

The primary differentiation between rhombuses and squares is that latter must have four interior right angles. Although the four interior angles of a rhombus must also equal a sum of 360 degrees, the interior angles inside of a rhombus do not need to be right angles. Instead, the adjacent interior angles of a rhombus must be supplementary angles.

By applying the perimeter formula, the solution is: 

\(\displaystyle 68=4S\)

\(\displaystyle s=\frac{68}{4}=17\)

Check:

\(\displaystyle 17\times4=68\)

Each side of the rhombus must equal \(\displaystyle 17\).

The perimeter formula for a rhombus is the same formula used to find the perimeter of a square. This is because both shapes, by definition, have \(\displaystyle 4\) equivalent sides. Thus, the total perimeter is the sum of all \(\displaystyle 4\) sides. 

The primary differentiation between rhombuses and squares is that latter must have four interior right angles. Although the four interior angles of a rhombus must also equal a sum of 360 degrees, the interior angles inside of a rhombus do not need to be right angles. Instead, the adjacent interior angles of a rhombus must be supplementary angles.

To solve this problem, apply the perimeter formula for a rhombus: \(\displaystyle P=4S\). 
By applying the perimeter formula, the solution is:

\(\displaystyle 352=4(s)\)

\(\displaystyle s=\frac{352}{4}=88\)

Check:

\(\displaystyle 88\times4=352\)

If the diagonals of a quadrilateral are perpendicular bisectors of one another, then the quadrilateral must be a rhombus, but not necessarily a square. Since all rhombi are also parallelograms, quadrilateral ABCD must be both a rhombus and parallelogram.

Two shapes are similar to each other if they are the same except for differences in scaling. This means that all of the angles of one shape have to be the same as the angles of the other shape, and all the sides have to be proportional to each other. For example, if we have two rectangles A and B, where A has side lengths 2 and 4, and B has side lengths 5 and 10, A and B are similar because the ratio between 2 and 4 is the same as the ratio between 5 and 10, and also the ratio between 2 and 5 is the same as the ratio between 4 and 10. Everything is proportional (and all the angles are the same) so the two rectangles A and B are similar.

The two rhombuses in our figure are not similar to each other, because we can see the larger angle in the rhombus on the left is not the same as the larger angle in the rhombus on the right. If we scaled the larger rhombus down and tried to cover up the smaller rhombus with it, it wouldn't work because they aren't proportional to each other.