Points A, B, and C are on sides WX, YZ, and XY of rectangle WXYZ as shown below such that XA = 4, YB = 18, angle ACB= 90 degrees, and YC = 2XC. Find AB.
**The answer is not 4sqrt31 or 2sqrt131
+2862 Can you at least present it properly? Remove or render those Latex markings, please!
+2862 I PRAY THAT YOU ACTUALLY READ MY ANSWER INSTEAD OF PLUGGING IT INTO YOUR HOMEWORK CHECKER
XC = \(x\)
CY = \(2x\)
Bash pythagorean theorem for sides AC and CB
AC:
sqrt(16 + x2)
CB:
sqrt(324 + 4x2)
AB2 = AC2 + CB2
(Substitute AC and CB)
(1) AB2 = 5x2 + 340
Draw a line from B to the other side of the rectangle that is parrelel to XY. Let's name the point on the other side \(p\)
\(bp\) is 3x
PA is 18 - 4 = 14
Pythagorean theorem once again!
(2) AB2 = 9x2 + 196
Oh wait! We have two equations that can be substituted! Yay!
Substitute (1) and (2)
9x2 + 196 = 5x2 + 340
4x2 = 144
x2 = 36
x = 6
Let's plug in X for AB
36 * 9 + 196
520
sqrt(520)
\(\boxed{2\sqrt{130}}\)
