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Number of equilateral triangles with $y=sqrt{3}(x-1)+2$ and $y=-sqrt{3} x$ as two of its sides, is(A) 0(B) 1(C) 2(D) none of these...

Question

Number of equilateral triangles with $y=sqrt{3}(x-1)+2$ and $y=-sqrt{3} x$ as two of its sides, is(A) 0(B) 1(C) 2(D) none of these

Number of equilateral triangles with $y=sqrt{3}(x-1)+2$ and $y=-sqrt{3} x$ as two of its sides, is (A) 0 (B) 1 (C) 2 (D) none of these



Answers

In the figure below, $A B C D$ is a square and $A E D$ is an equilateral
triangle. If $A B=2,$ what is the area of the shaded region?
$$\begin{array}{l}{\text { (A) } \sqrt{3}} \\ {\text { (B) } 2} \\ {\text { (C) } 4-2 \sqrt{3}} \\ {\text { (D) } 4-\sqrt{3}}\end{array}$$

So Triangle X y Z has to be in a sauce Elise triangle. So let's take a look at it. We have X, we have X and Y down here and then we have Z at the top. So X and Y are both mid points there at the same level. There are always going to be at the same level. Z is the only thing that's changing. So while de changes, these sides are actually going to change at the same rate of each other while this side is gonna be in a separate in the separate little plane of its own, so it has to be a sauces.

We're told that the length of a side of an equilateral triangle is for and we need to find what type of number represents the length of the altitude of the triangle. So let's catch it out. We have an equilateral triangle. Redo that, and each side is for because it's an equilateral triangle, all sides have the same length. The altitude of the triangle is just this line right here. The value right here is half of four, which is this too. We consult for the altitude of the triangle by applying the Pythagorean theorem. We know that the high pot news, which is four so four squared equals both of the leg squared added together, which is two squared plus altitude. I'll call that a thing squared. So 16 equals four plus a square, so 12 equals a squared or a equals the square root of 12. Now let's see what type of number describes this value? A. Is it a natural number? Ah, whole number or an imager? Well, the natural numbers are the positive counting numbers, and the whole numbers are the natural numbers, including zero. And the managers are the natural numbers. They're opposites and zero aid doesn't think any of these because it is. It's a square root of 12. It is also it is also not a rational number because irrational number is a number that can be expressed by a fraction of an integer divided by another integer when you have a square root, the only way that number is natural is if the number inside this query is a perfect square. 12 is not a perfect square, so we know that the square root of 12 is not irrational number. So we know that the type of number that best describes the length of the altitude is an irrational number, which I believe his answer. Choice D. Our final answer is D irrational number.

Hello. Welcome. That's lesson. We've been given some or into a triangle. Three points? Yeah. Why? So these are the points given to us. It would be nice to find whether triangles an equilateral triangle on the electorate triangle. Then the side A B would be equal to the side A c which wouldn't can be called to the size bc. Okay, so let's find out. So for the four, let's George Triangle a bleeder. Growing will help us. A big Oh, mhm. Lose the white as this does the X this one, 234 Yeah. Okay, Yeah. Okay, so the first point is 00 the second point. Iss one school it off. Theresa. Schools of three is 1.7. So one 17 b. Yeah, probably. Yeah. Then two in jail. That is here. So this is a quiet triangle has to find. Sure. Okay. Hello. So the Syed a b when we call the skirt off zero minus one squared glass. Their oneness Scoot off, Troy squared. And that is screwed off One last straight. So it's called four is too part. The next one is a C. That is a square root off. So we take the the X component. The difference of the X component squared. That's the difference of the why cos squared. So the zero minus two was quite class zero minus zero. Almost quit. So that is to to negative two square that is 40 or two to home. The last one is BC, and that iss one my nest to r squared, then scoot off. Three minus zero was great so that ISS stood off one last three. Let's go this very giant and that is go to us. Well, so find out that a b a c N b c oh, the same. And because you're all the same, we have a triangle with that three sides equal. So the a b c or equal that makes it ache. Electoral Collateral Triangle? Yes. Okay. All right. So until time


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