Areas of triangles
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Triangle missing side example
- [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.