solve for x similar triangles

Answer:x = √75Step-by-step explanation:We can write out all relations of each triangle here using the Pythagorean theorem (there are 3 triangles total). The triangles are ABD, BCD, and ABC.For triangle ABD: AB² = AD² + BD²AB² = (AC - DC)² + BD²y² = (15 - 5)² + BD²y² = 100 + BD²For triangle BCD:x² = BD² + 5²x² = BD² + 25For triangle ABC:15² = x² + y²225 = x² + y²From here we can substitute into the equation ABC. We can substitute x² and y² with our first and second equations.225 = BD² + 25 + 100 + BD²225 = 2BD² + 125100 = 2BD²50 = BD²We don't need to solve for BD, we can substitute it into our equation for triangle BCD to solve for x.x² = BD² + 25x² = 50 + 25x² = 75x = √75