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# help me. thank you

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386
7  What is the value of x?

Apr 28, 2018
edited by AgentFatboy  Apr 28, 2018

### 7+0 Answers

#1
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The length of $$AB$$ & $$BC$$ are 6. This is because the hypotenuse of a right-isosceles triangle is $$\frac{h}{\sqrt{2}}.$$

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Apr 28, 2018
#2
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From this, you know that $$AB\Xi BC$$ and the values are $$\frac{6\sqrt{2}}{\sqrt{2}} = 6.$$

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Apr 28, 2018
#3
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If AB is 6, then 6 is the side of a 30-60-90 triangle or a half-cut equilateral triangle. This would mean that x is half of 6 or x is 3.

Apr 28, 2018
#4
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I had to write my answer in multiple posts since LaTeX hates me right now. I might be wrong so make sure to double check my work. Good Luck!

Apr 28, 2018
#5
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Your very much welcome!

Apr 28, 2018
#6
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$$AB=BC \qquad\text{ABC is a right angled isosceles triangle}\\ 2*(AB)^2=(6\sqrt2)^2\\ 2*(AB)^2=72\\ (AB)^2=36\\ AB=BC=6$$

$$cos 60=\frac{1}{2}$$

$$\frac{x}{6}=\frac{1}{2}\\ x=3$$

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Apr 28, 2018
#7
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Or you can write it in 1 post, good thinking!

Apr 29, 2018
edited by TheMathCoder  Apr 29, 2018