[tex]\begin{gathered} \text{Note since it's a paragellogram then we have.} \\ ED\text{ = }\frac{1}{2}\times BD \\ 7x\text{ = }\frac{1}{2}\times(16x-38) \\ 7x\text{ =}\frac{(16x-38)}{2} \\ By\text{ cross multiplying we have.} \\ 7x\text{ }\times\text{ 2 = 16}x\text{ -38} \\ 14x\text{ = 16}x\text{ - 38} \\ By\text{ collecting like term we have.} \\ 14x-\text{ 16}x\text{ = -38} \\ -2x\text{ = -38} \\ x\text{ = }\frac{-38}{-2}\text{ = 19} \\ x\text{ = 19} \\ \text{Therefore, BD = 16}x\text{ - 38} \\ \text{ BD = 16}\times19\text{ - 38} \\ \text{ BD = 304 - 38} \\ \text{ BD =}266 \end{gathered}[/tex]
