Answer:
x = √75
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 + BD²
AB² = (AC - DC)² + BD²
y² = (15 - 5)² + BD²
y² = 100 + BD²
For triangle BCD:
x² = BD² + 5²
x² = BD² + 25
For triangle ABC:
15² = x² + y²
225 = x² + y²
From here we can substitute into the equation ABC. We can substitute x² and y² with our first and second equations.
225 = BD² + 25 + 100 + BD²
225 = 2BD² + 125
100 = 2BD²
50 = BD²
We don't need to solve for BD, we can substitute it into our equation for triangle BCD to solve for x.
x² = BD² + 25
x² = 50 + 25
x² = 75
x = √75