Question

What are the values of x and y?

Answer 1

Based on AA Theorem, which says that if the two given angles of both triangles are equal, then they are similar, in this case, triangle ADB and triangle BDC are similar.

If two triangles are similar, that means their side length are proportional.

Let us first solve for x:

`(BD)/(DC) =(AD)/(DB) \\(9)/(x) =(12)/(9) \\12x = 81\\x = 6.75\\\\`

Now using the pythagorean theorem, we get that

`y^(2) =x^(2) +9^2 = 6.75^2+9^2=126.5625\\y = √(156.5625) \\y=11.25`

So x = 6.75 and y = 11.25

Hope that helps!