Answer:
x= 9
Explanation:
Please see the attached picture.
In △BCD
∠BDC= 180° -90° (adj. ∠s on a str. line)
∠BDC= 90°
Applying Pythagoras' Theorem,
(BD)² +(DC)²= (BC)²
(BC)²= 6² +4²
(BC)²= 52 -----(1)
In △ABD
Applying Pythagoras' Theorem,
(AD)² +(BD)²= (AB)²
(AB)²= x² +6²
(AB)²= x² +36 -----(2)
In △ABC
Applying Pythagoras' Theorem,
(AB)² +(BC)²= (AC)²
(AB)² +(BC)²= (x +4)²
Substitute (1) and (2):
x² +36 +52= (x +4)²
x² +88= x² +2(x)(4) +4² (simplify, expand)
x² +88= x² +8x +16
8x +16= 88 (-x² on both sides)
8x= 88 -16
8x= 72
x= 72 ÷8
x= 9