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Of the hypotenuse; X if (20,21,x) isa Fythagorean triple? What is the length0 2229 4142...

Question

Of the hypotenuse; X if (20,21,x) isa Fythagorean triple? What is the length0 2229 4142

of the hypotenuse; X if (20,21,x) isa Fythagorean triple? What is the length 0 22 29 41 42



Answers

The leg lengths of a $30^{\circ}-60^{\circ}-90^{\circ}$ triangle are given. Find the length of the hypotenuse. $$7 \text { and } 7 \sqrt{3}$$

For this question, we're asked if I am the life of our positive this week of a triangle with Silence three and 27. So we can just use our hyper Pichai on intelligence. Trace very plus reads 27 squared is equal to or her party squared so we can say that's nine plus 27 is able to. Each squared, which gets each squared, is equal to 36. Getting its H is equal to six.

I need to figure out what the dimensions of my legs are. My legs, but the legs of the triangle, this right triangle and I have written down the information that I was given in the problem. And I'm gonna use the Pythagorean theorem to solve this, and it's gonna create a quadratic for me, and I'm gonna probably have to use the frenetic formula, but we'll see, See, May not have to. So the first thing going to do is I'm gonna write down Pythagorean Theory, which says a squared plus B squared equals C square. So the sum of the squares of the two legs of a right triangle equals the square of its hypotheses. So I'm gonna substitute the values so I have a right, so a square and I don't know what day is it Z written as a variable. But it tells me I do know that my other leg B is one more than twice of the short, short of side. So if I double this short side and add one, that's gonna be my be, so I'm actually gonna substitute that in some ready be in terms of a so in terms of A B is to a plus one squared, and I have my see value as radical 29 square. And so now all I'm gonna do is I'm just going to expand this all out ace. Nope. Don't like it a squared. All right, so now I'm gonna foil so to eight times to A is for a square 28 times one is two a one times two a is to a and one times one is one and radical, 29 square is 29. Now I'm gonna combine some like terms. So I have won a squared and for a squared, which is, I think missing might need to me batteries five a square. I have two A's and two more days. So I have four A's and then I have my constant plus what? And now I'm going to subtract 29 from both sides, and that's gonna leave me with five a square plus four. A minus 28 equals zero, and I really don't want to try and have to factor that. So instead I am going to use the quadratic formula. Well, the quadratic formula is X equals negative B plus or minus the square with B squared minus four a c oh, over to a. And now I'm gonna identify my a and B and C values. So here my A value is the coefficient of my square term. So that would be five. My be value is the coefficient of mine in your term Or that second term, which here is for and my see value is my constant. So this third term here is negative. 20. So now I'm gonna sit on substitute those into the formula. Thanks. It was located be plus ra minus the square root be spared. Minus four. Okay. See? Oh, over to a All right. So this is gonna leave me with negative. Four was negative. One times four is night before, and four squared is 16 and four times five is 20 and two times five is 10. So now I have negative for plus or minus 20 times 28. And because they're both negative, I get a positive number 560 over 10. So now I get to add 16 and 560 which is 67 five 576 over text, and I am going to factor 576 because it may or may not, But it may end up being that there are some perfect squares that I can factor out of that. So I'm actually gonna do that way over here. In fact, I'll do the different color. Just so it kind of stands out, I'll put a little star by it. All right? So 576 let's factor that, um, maybe four. I don't know. I'm no to, So I might just get a bunch of twos, so it's gonna be to 80 a. Um, I think I don't mess this up five. Well, I suppose I could always look and say that is a perfect square. I don't. Oh, it is, huh? Looked save ourselves in trouble. Eso It is a perfect square if you put it in and you check it so I don't have to do that. Uh, it is 24 that is the square root of 576. So I now have negative four plus or minus 24/10 and I'm going to continue this over here. And that means that I can either do. Let's see, I'll do that. Look, I need to go back to the pen. I will do X equals negative for plus 24/10. And that is gonna be negative. Four plus 24 is 20/10. 20. Divided by tennis, too. The other thing that can happen is I can get negative for minus 24 over 10. Negative. Four minus 24 is negative. 28 over 10. And that's gonna equal negative 2.8. So, um, X can either be sorry for that. Um, excuse me to be two or negative. 2.8. Well, here's the problem. Um, we're talking about a sidelight here and the side. Life can't be negative. So what we need to do is we need to substitute that value of the positive ones of, So it's gonna cross this out here, right? So when When we're saying that this is access is really a that value of the the side, like so we're gonna use to. And now we have to just substitute that in there. So a is to That's my rational solution. And then I have two times two plus 12 times two is 44 plus one is five. So is to B. Is five. See? Is radical. 29

And this problem were given the two legs, so that would be a and B in the Pythagorean theorem, which I substituted in. So then I square 32 which is 1024. I square 24. Add those two together. Use me 1600 equals C squared, which means if I take the square root of 1600 that's going to give me see if a number square to 1600 than this, where we do that number would give me see that would give me 40 equals C. Since my labels here inches see the high pot news here would be 40 and that would be in inches.

So in the U. N. Question we have the length of, then it's up two sides of a right angled triangle Right? So it has given us is equal to seven which is one side, and B. Is equal to 24. And we are told to find the length of the hypotenuse which is the longest side of a right triangle, right? So this is the high parties, let's name the site as it's alright. So to find edge, we can use the pythagorean theorem according to which we can write that the length of high powered news of uh hyper news in a right triangle can be found as H is equal to the square foot of sum of squares of the other two sides. So the square root off sum of squares of A. And B. So we can use this formula to find the length of the hyper genius as square root of seven squared plus 24 squared. And this is equal to the square root of seven squared is 49 and the square group square, the seven square is 49 24 square is 5 76 So this is equal to the square root of 625. So when we take the square root off 625, We get the answer as 25 units. So the required length of the hyper dinosaur here is 25. So I hope you understood the answer tandem.


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