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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

 Mar 24, 2020
edited by Guest  Mar 24, 2020
 #1
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Can you at least present it properly? Remove or render those Latex markings, please!

 Mar 24, 2020
 #2
avatar+2854 
+1

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 = 5x+ 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)

\(\boxed{2\sqrt{130}}\)

.
 Mar 24, 2020

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