Question

Solve for X, Similar triangles

Answer 1

Answer:

x = √75

Step-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 + 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