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CCSS.Math:

the formula for the area of a triangle is a is equal to one-half B times H where a is equal to area B is equal to length of the base and H is equal to the length of the height so area is equal to 1/2 times the length of the base times the length of the height solve this formula for the height so just to visualize this a little bit let me draw a triangle here let me draw a triangle just so we know what it B and H are B would be the length of the base so this distance right over here is B and then this distance right here this distance right here is our height that is the height of the triangle you did a lowercase H because that's how we wrote it in the formula now they want us to solve this formula for the height so the formula is area is equal to 1/2 base times height and we want to solve for H we essentially want to isolate the H on one side of the equation it's already on the right hand side so let's get rid of everything else on the right hand side so we could do it well I'll do it one step at a time we could kind of skip steps if we wanted to but let's see if we can get rid of this one half so the best way to get rid of a 1/2 and it's being multiplied by H is if we multiply both sides of the equation by its reciprocal if we multiply both sides of equation by two over one or by two so let's do that so let's multiply remember anything you do to one hit one side of the equation you also have to do to the other side of the equation now what did this do well the whole point behind multiplying by 2 is 2 times 1/2 is 1 so on the right hand side of the equation we're just going to have a be H and on the left hand side of the equation we have a 2 a 2 a and we're almost there we have a be multiplying by an H if we want to just isolate the H we could divide both sides of this equation by B we're just dividing both sides you can almost view B as the coefficient on the H we're just dividing both sides by B and then what do we get well the right hand side the B's cancel out on the left hand side we're just left with 2a over B so we get H and I'm just swapping the sides here H is equal to 2a over B 2 a over B and we're done we have solved we have solved this formula for the height and I guess this could be useful if someone just gave you a bunch of areas and a bunch of base lengths and they said keep giving me the height for those values for those triangles