To find the length PD we must first find the value of x. First, by the Segment Addition Postulate, we can express the diagonal DB as the sum of PB and PD.
DB= PB+PD
For all rhombi, the diagonals bisect each other. Therefore, the lengths of PB and PD are equal. We can use this fact to rewrite the Segment Addition Postulate equation in terms of the given expressions, DB= 2x-4 and PB=2x-9.
Finally, we can find PD using the value of x we found. As previously mentioned, we know that the lengths of PB and PD are equal. Therefore, we can use the given expression for the length of PB to find PD.
lPD=PB PB=2x-9 ⇒ PD=2x-9
Let's substitute x=7 into this equation to find PD.
