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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 all right 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 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 going to rotate it so if I rotate the o 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 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 our the length of our base then our the height the height of our triangle is going to be tell me if you 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 could say 75 is equal to 1/2 times 10 is equal to 5 times X is equal to 5 times you 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 take 5 times what is equal to 75 and you might be to figure that out you might say okay let's see five times ten is fifty and then let's see I need another 25 so I put another five there so it's really five times 15 or you could do a little bit system or systematically you can divide both sides by what you're multiplying by X so if you divide this sides by 5 5 times X divided by 5 while you're just going to have an X left over 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 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