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Triangle missing side example

Sal Khan explains how to find the missing side of a triangle when given its area and two other side lengths. By using the formula for the area of a triangle (1/2 base x height), we can solve for the unknown side length.

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  • starky tree style avatar for user Wolf LEX
    so confusing cant you just do b times h divided by 2
    (15 votes)
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    • duskpin ultimate style avatar for user tiannaduffin
      Yes u can, but only if you know the base and height. This skill is about figuring out the missing base/height when you are given the base/height and the area of the triangle

      As an example, let's say the base was 10 and the area was 300. We need to find the missing height. The formula to figuring out the area of a triangle is
      (b * h) / 2. Therefore, (10 * h) / 2 = 300, and
      (10 * h) = 600. 600 / 10 is 60, so h is 60, as
      (10 * 60) / 2 = 300 and (10 * 60) = 600
      (14 votes)
  • aqualine ultimate style avatar for user Moon
    I don't understand why math is so hard
    (15 votes)
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  • starky sapling style avatar for user brandon.edwards
    So I paused the video and tried to do it myself, I got the answer right, but I did it differently. I just wanted to make sure it would always work in a situation like this. So I divided 75 by 10 and got 7.5, knowing that this is actually 1/2 the base, multiplied this by 2 and got 15, sounds like a lot, but only took me about 1 minute to do compared to your way, which is why I wanted to know if it was a correct way of doing it.
    (9 votes)
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  • aqualine ultimate style avatar for user Austin
    So to find the missing side its just the area divided by half of the hight
    (5 votes)
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  • boggle yellow style avatar for user Damien
    Why is 11 there if we don't need it? They're scamming us, that's illegal in my book.
    (7 votes)
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  • blobby green style avatar for user Madison Newman
    How do I work out the area of a triangle if I’m given only one short side length
    (7 votes)
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  • aqualine ultimate style avatar for user Midnight_Robluxidude999
    I have a question for everybody:
    "How did you guys get through all this hard strategy of math and even get the hang of it? It's weird."
    Everybody says that it is hard but how come you guys know the answer on this whatever area of triangles and the missing side. It is very confusing to me even with the video.
    Can you guys please help me because, and yes, I do know that you have to go through other "EASIER" strategies of math in order to understand harder ones but please comment and tell me the answer to this question.
    (5 votes)
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  • leafers seedling style avatar for user TenaciousPumpkinKiddo
    Can someone please give me with an short equation for this?
    (2 votes)
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  • aqualine ultimate style avatar for user Midnight_Robluxidude999
    Who even invented this type of math strategy and these units? And why?
    (3 votes)
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  • eggleston blue style avatar for user EH
    No matter how many times I listen to this, I never understand! Please help! I have a math test next month!
    (2 votes)
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Video transcript

- [Instructor] The triangle shown below has an area of 75 square units. Find the missing side. So pause the video and see if you can find the length of this missing side. Alright, now let's work through this together. They give us the area, they give us this side right over here, this 11. They give us this length 10, which, if we rotate this triangle you can view it as an altitude. And in fact let me do that. Let me rotate this triangle, because then I think it might jump out at you how we can tackle this. So let me copy and let me paste it. So if I move it here, but I'm gonna rotate it. So if I rotate, that is our rotated triangle and now it might be a little bit clearer what we're talking about, this length x that we want to figure out, this is our base. And they give us our height and they give us our area. And we know how base, height and area relate for a triangle. We know that area is equal to 1/2 times the base times the height, and they tell us that our area is 75 units squared. So this is 75 is equal to 1/2. What is our base? Our base is the variable x. So let's just write that down. 1/2 times x and then what is our height? Well, our height is actually the 10. If x is the length of our base, then the height of our triangle is gonna be 10, we actually don't even need to use this 11. They're putting that there just to distract you. So, this is going to be our height, times 10. So 75 is equal to 1/2 times x times 10, or, let me just rewrite it this way. We can say 75 is equal to 1/2 times 10 is equal to five times x is equal to five, let me do the x in that same color, is equal to five times x. So what is x going to be? There's a couple of ways you could think about it. You could say five times what is equal to 75? And you might be able to figure that out. You might say, OK, five times 10 is 50, and then let's see, I need another 25, so put another five there, so it's really five times 15, or you could do it a little bit more systematically. You can divide both sides by what you're multiplying by x. So if you divide this side by five, five times x divided by five, well, you're just going to have an x left over. But these two things were equal, so you can't just do it to one side, you have to do it to both sides. So you have to divide both sides by five. And what's 75 divided by five? Well that is 15. So you get x is equal to 15. And you can verify that. If x is equal to 15, base times height times 1/2. Well, it's 15 times 10 times 1/2, or 15 times five which is going to be 75 square units.