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Need help with a math problem


Hambone

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I am helping my daughter with her math homework. We can figure them all out except one. Since the folks on this forum are the smartest people on the face of the earth, I thought you might be able to assist. Here it is.

 

If the height of a triangle with a base of 8 inches is tripled, it's area is increased by 96 square inches. Find the height of the triangle.

 

I know that the area of a triangle is, 1/2 base x height. It just doesn't seem like there is enough information there to get the answer. Maybe I am just having a brain fart.

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I am helping my daughter with her math homework. We can figure them all out except one. Since the folks on this forum are the smartest people on the face of the earth, I thought you might be able to assist. Here it is.

 

If the height of a triangle with a base of 8 inches is tripled, it's area is increased by 96 square inches. Find the height of the triangle.

 

I know that the area of a triangle is, 1/2 base x height. It just doesn't seem like there is enough information there to get the answer. Maybe I am just having a brain fart.

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My equation is slightly more crude than Jimbob's, but perhaps slightly more comprehensible:

 

Let H=original height of the triangle

 

1/2(8H)=3[1/2(8H)]-96

4H=12H-96

H=3H-24

-2H=-24

H=12

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Or a little simpler, I think: you have two unknowns, the original height of the triangle (call it "h"), and the original area of the triangle ("a"). You know that half of the quantity base times height is the area, so a = (8*h)/2, and (a + 96) = (24*h)/2 ("24" coming from 8*3*h).

 

Solve the first for "a" in terms of "h", which is just completing the division by two on the right hand side, so a = 4*h. Then substitute that into the second equation:

 

4*h + 96 = (24*h)/2

 

...and solve (complete division by 2 on the RHS to get 4h + 96 = 12h, subtract 4h from each side to get 96 = 8h, divide by 8 and h = 12).

 

That's nothing different from what anyone else did above me...but it might be clearer to some people the way I wrote it out.

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well, since we're talking about he we solved the problem individually...

 

We know...Triangle2 = Triangle1 + 96

We know...The formula for a triangle, bh/2

We know...The height of Triangle2 is 3 times Triangle1

We know...The base of Triangle1 = The Base of Triangle2 = 8

 

Therefore...we can take the formula of a triangle and conclude the area of Triangle1 is bh/2

Therefore...we can also take the formula of a triangle and conclude the area of Triangle2 is (b * 3h)/2

 

Giving us...

(b * 3h) / 2 = bh/2 + 96

 

Get all of your unknowns on one side of the equation and all of your knowns on the other, so subtract bh/2 from both sides...

(b * 3h) / 2 - bh/2 = 96

 

Plug in your known variable, b = 8...

(8 * 3h) / 2 - 8h/2 = 96

 

Do some multiplying...

24h/2 - 8h/2 = 96

 

Bit of division...

12h - 4h = 96

 

Bit of subtraction...

8h = 96

 

And finally a bit more division..

h = 12

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Doesn't matter.  All triangles have an area of half the base times height.

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Ooops....& you just know I mucked around then figuring out you are correct. :D

:angry:

....& I used to be a math wizz. :devil:

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