We want to find the length AP. Let's analyze the given rhombus.
We are given the lengths AB=15 and PB=12. Note that the diagonals in a rhombus are perpendicular. Therefore, â–ł ABP is a right triangle with legs AP and PB, and hypotenuse AB. We can use the Pythagorean Theorem to calculate AP.
AP^2+PB^2=AB^2
⇕
AP^2+12^2=15^2
Let's solve the above equation for AP.
Note that, when solving the above equation, we kept the principal root. This is because AP is a side length and therefore must be positive. We found that AP= 9.
