Question

explaining a process
how can you find the perimeter of the rhombus?
find \\( \frac { 1 } { 2 } ( q s ) ( r t ) \\).
find \\( \frac { 1 } { 2 } ( q t ) ( t s ) \\).
use the distance formula to find qt, then multiply by
4.
use the distance formula to find qt and qr, add
the distances, then multiply by 4.

Explanation:

Step1: Recall the property of a rhombus

A rhombus has all four sides equal.

Step2: Analyze each option

• Option 1: $\frac{1}{2}(QS)(RT)$ gives the area of the rhombus (using the formula for area of a rhombus with diagonals $d_1$ and $d_2$: $A=\frac{1}{2}d_1d_2$, where $QS$ and $RT$ are diagonals), not the perimeter.
• Option 2: $\frac{1}{2}(QT)(TS)$ is not a valid formula for perimeter or area of a rhombus.
• Option 3: Since all sides of a rhombus are equal, if we use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ to find the length of one side (say $QT$), then the perimeter $P=4\times$ (length of one side).
• Option 4: We don't need to find two - different side lengths (because all sides of a rhombus are equal). Adding two side lengths and multiplying by 4 is incorrect.

Answer:

Use the distance formula to find QT, then multiply by 4.