Question

can someone please step by step explain the answer

Answer 1

Answer:

$x = \frac{3}{2}$

Step-by-step explanation:

Let us first name the points in the triangle,

The topmost point is A,

the leftmost point is B,

and the rightmost point is C,

and the point from A on BC is D

So, using Pythagoras Theorem in triangle ADC,

AC² = AD²+DC²

AC² = 3² + 6² = 9+36 = 45

AC = 3√5

Now, using Pythagoras Theorem in triangle ABC,

BC² = AB²+AC²

(6+x)² = AB² + 45

AB² = (6+x)²-45

using Pythagoras Theorem in triangle ABD,

AB² = AD²+BD²

(6+x)²-45 = 9+x²

36 + x² +12x = 54 + x²

12x = 18

x = 3/2

Hope this was helpful. Please mark me as brainliest!!