Equilateral triangle xyz is cut in half by line segment xp where point p is the midpoint of yz. if xy=6, what is the length xp? a) 6√2 b) 3√3 c) 3√2 d) 4 e) 3

Your answer is B) 3√3.

We can find this by drawing out the triangle and seeing that because it is equilateral, YZ would also equal 6, meaning that YP would equal half of 6, making it 3.

This allows us to draw a right angled triangle using YP as 3, and XY as the hypotenuse as 6. Because it is a right triangle we can therefore use Pythagoras's Theorem c² - b² = a² and do 6² - 3² = 36 - 9 = 27.

Finally, we need to square root 27, which we can do by finding the square number 9 inside it and writing √27 as √9 × √3 = 3√3.

I hope this helps! Let me know if you have any questions :)

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