About this video
A triangle has area 75 square units, a side of 11 and a height of 10, and one side x is missing. Rotating the triangle shows x is the base with height 10, so 75 = 1/2 x x x 10 = 5x, giving x = 15. The 11 is a distractor.
You'll be able to
- match the base of a triangle with its height.
- set up an equation from area = 1/2 x base x height.
- solve an equation like 5x = 75 to find a missing side.
- check my answer by putting it back into the formula.
Key words
- altitude
- Another word for the height of a triangle, drawn at a right angle to the base.
- base
- The side the height is measured to.
- rotate
- Turn a shape around without changing its size.
- verify
- Check an answer is right by using it in the original problem.
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 could 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 the, oh, 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, they tell us that our area is 75 unit 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 lemme just rewrite it this way. We could say 75 is equal to 1/2 times 10 is equal to 5 times x, is equal to 5 times, lemme do the x in that same color is equal to 5 times x.
So what is x going to be? There's a couple of ways you could think about it. You could say 5 times what is equal to 75 and you might be able to figure that out. You might say, okay, let's see, 5 times 10 is 50. And then let's see, I need another 25. So I'd put another 5 there. So it's really 5 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 5, 5 times x divided by 5, well you're just going to have an x leftover. But you can't, 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 5. And what's 75 divided by 5? Well that is 15. So you get x is equal to, 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 5, which is going to be 75 square units.
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