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

Guest Mar 24, 2020

edited by
Guest
Mar 24, 2020

#1**0 **

Can you at least present it properly? Remove or render those Latex markings, please!

CalculatorUser Mar 24, 2020

#2**+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 + x^{2})

CB:

sqrt(324 + 4x^{2})

AB^{2} = AC^{2} + CB^{2}

(Substitute AC and CB)

**(1) AB ^{2} = 5x^{2 }+ 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) AB ^{2} = 9x^{2} + 196**

Oh wait! We have two equations that can be substituted! Yay!

Substitute **(1) and (2)**

9x^{2} + 196 = 5x^{2} + 340

4x^{2} = 144

x^{2} = 36

x = 6

Let's plug in X for AB

36 * 9 + 196

520

sqrt(520)

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

.CalculatorUser Mar 24, 2020