Step-by-step explanation:
The lengths of the sides of a triangle are 3t, 5t - 12, and t + 20 . a. Find the value(s) of that t make the triangle isosceles. b. Does any value of make the triangle equilateral?
As you can see, I have my subsidies trying out and, like, a lot of time president focused on assessing. Okay, so we need to figure out what seat for the size that we're giving you could put them in any order you want. So we're gonna try this order for us, and then we're gonna try. So we're gonna do you know that the inside of the a softly triangle in this out of this triangle are equal to each other. And when you add them together, there has to be greeted with this out of this. Had a trying. So we're first gonna do three t is equal to five t oneness. Well, arguments of drugs five from both sides fascinate this negative to t is equal to negative. After this, we could divide negative to on both sides to find out what see is to get T bites so tracked, divided by negative tune. And then we're gonna do t is equal to negative 12 of our negative to 6 36 So we're going to check our solution by plugging in six. So when we plug six into this equation, we're gonna gate 18 3 times six is 18. And when we plug six into this equation, we're gonna get five times six, which is dirty five times six is 30 and you're going to subtract. Told him 30 that gave to. And then we're gonna put 6 40 and we're gonna add it to Tony, which is 26. And then after this, we're gonna add these two 18 18 to figure it out if it's hired into 6 18 plus 18 is 36. So it's harder 26 c is equal to is equal to six. Like I said before, this is not the only order because switch up the sides with them in different places. So I'm gonna take away this side. I took a week this, and I'm gonna put I want to take with this ad too, and I'm in. I'm gonna put t this 20 this side and five C minus. Whoa, This Okay, so we're gonna do the same thing we did over here. We're gonna do three t is equal to C plus 25 because these two sides great. See? Do you see before? See e waas 20 first. We're going to subtract C from both sides we're gonna get to t is equal to finding. And then we're gonna divide to from both sides to get by itself. And, uh, an anti is equal to 10 because 20 the bottom right to it. So we also know that he gave me 10. So we're gonna plug 10 in today, San plus 10 times their times three is equal to this is dirty. And we also know we're gonna put 10 for this side. A tent was 20 is dirty also, it's an end times what? It's 50 When you subtract well, you get 36. No, you get 30 feet, you get 38 when you add 30 plus dirty is 60. So this works. So t is also equal to 10 and we're gonna switch up the order again. This sound this one, I believe this one. And also as you know, we're switching at the side, trying all the possible leads with right. Let's go drop this trying. So this side now will be treaty. And this I will be five c minus slow. We're gonna go. We're gonna do five minutes. 12 is equal to 10 is equal city plus 20 because we know these two sides has equal five feet on its 12. I just love equal See loose. Okay, As you can see, we're going to subtract, see from both sides. And I was going to or C and I'm going to do two steps at a time for gonna actual on this side to everything this tool to get rice on one side of the equation. So I'm gonna add so so both side, and it's gonna before C is equal to dirty, too. We're gonna divide both sides by four to get see bites. So four divided by 36 is line for teeth equal to nine. We're gonna plug that incident equation tee. Times five is nine times five is 45. We're gonna subject for from him that is equal to 32. 33 and then we're gonna do nine waas 20. So amid a misty 2012 is actually 32. So these so t is actually equal to eight because three times 32 divided by four is eight. And we're gonna redo this one because so eight times five is 40 eight times five is sporting. And when we take away Whoa. 40 minus 12 is 28 is doing a So we're gonna do and we're gonna put in April. See here too. This is gonna be a plus 20 which is 28. We're gonna plug in eight for decide eight times three is 24 24. And as you see, this is obviously lower. It's gonna be lowered, indecent. Act together. So, you know, seek and also equal to eight. So for the sausages triangle there. Three possible answers for teeth, depending on how you put the sides which side before, which in just it depend on how you put your sides for the collateral. We know that all of the size has to equal to one thing. And from this, the signs don't equal the same thing One of them is You could get two of them to equal to each other so you can get rid of the size to be able to the same thing. So for the equilateral triangle, it's not possible. So not
